Qucs
A Tutorial
Modelling Operational Amplifiers
Mike Brinson
c 2006, 2007 Mike Brinson <mbrin72043@yahoo.co.uk>
Copyright Permission is granted to copy, distribute and/or modify this document under the
terms of the GNU Free Documentation License, Version 1.1 or any later version
published by the Free Software Foundation. A copy of the license is included in
the section entitled ”GNU Free Documentation License”.
Introduction
Operation amplifiers (OP AMP) are a fundamental building block of linear electronics. They have been widely employed in linear circuit design since they were
first introduced over thirty years ago. The use of operational amplifier models for
circuit simulation using SPICE and other popular circuit simulators is widespread,
and many manufacturers provide models for their devices. In most cases, these
models do not attempt to simulate the internal circuitry at device level, but use
macromodelling to represent amplifier behaviour as observed at the terminals of a
device. The purpose of this tutorial note is to explain how macromodels can be
used to simulate a range of the operational amplifier properties and to show how
macromodel parameters can be obtained from manufacturers data sheets. This
tutorial concentrates on models that can be simulated using Qucs release 0.0.9.
The Qucs built-in operational amplifier model
Qucs includes a model for an ideal operational amplifier. It’s symbol can be found
in the nonlinear components list. This model represents an operational amplifier
as an ideal device with differential gain and output voltage limiting. The model is
intended for use as a simple gain block and should not be used in circuit simulations
where operational amplifier properties are crucial to overall circuit performance.
Fig. 1 shows a basic inverting amplifier with a gain of ten, based on the Qucs OP
AMP model. The simulated AC performance of this circuit is shown in Fig. 2.
From Fig. 2 it is observed that the circuit gain and phase shift are constant and
do not change as the frequency of the input signal is increased. This, of course,
is an ideal situation which practical operational amplifiers do not reproduce. Let
us compare the performance of the same circuit with the operational amplifier
represented by a device level circuit. Shown in Fig. 3 is a transistor circuit diagram
for the well known UA741 operational amplifier1 . The gain and phase results for
the circuit shown in Fig. 1, where the OP AMP is modelled by the UA741 transistor
level model, are given in Fig. 4. The curves in this figure clearly illustrate the
differences between the two simulation models. When simulating circuits that
include operational amplifiers the quality of the OP AMP model can often be
a limiting factor in the accuracy of the overall simulation results. Accurate OP
AMP models normally include a range of the following device characteristics: (1)
1
The UA741 operational amplifier is one of the most studied devices. It is almost unique in
that a transistor level model has been constructed for the device. Details of the circuit operation
and modelling of this device can be found in (1) Paul R. Grey et. al., Analysis and Design
of Analog Integrated Circuits, Fourth Edition, 2001, John Wiley and Sons INC., ISBN 0-47132168-0, and (2) Andrei Vladimirescu, The SPICE book, 1994, John Wiley and Sons, ISBN
0-471-60926-9.
1
Equation
R3
R=47 k
Vin
OP1
G=1e6
Eqn1
d1=dB(Vout.v)
d2=phase(Vout.v)
Vout
V1
U=1 V R4
R=4.7 k
dc simulation
ac simulation
DC1
AC1
Type=log
Start=1 Hz
Stop=100 MHz
Points=801
Figure 1: Qucs schematic for a basic OP AMP inverting amplifier:Qucs OP AMP
has G=1e6 and Umax=15V.
DC and AC differential gain, (2) input bias current, (3) input current and voltage
offsets, (4) input impedance, (5) common mode effects, (6) slew rate effects, (7)
output impedance, (8) power supply rejection effects, (9) noise, (10) output voltage
limiting, (11) output current limiting and (12) signal overload recovery effects. The
exact mix of selected properties largely depends on the purpose for which the model
is being used; for example, if a model is only required for small signal AC transfer
function simulation then including the output voltage limiting section of an OP
AMP model is not necessary or indeed may be considered inappropriate. In the
following sections of this tutorial article macromodels for a number of the OP AMP
parameters listed above are developed and in each case the necessary techniques
are outlined showing how to derive macromodel parameters from manufacturers
data sheets.
2
Vout.v
0
-10
-20
1
10
100
1e3
1e4
Frequency Hz
1e5
1e6
1e7
1e8
1
10
100
1e3
1e4
Frequency Hz
1e5
1e6
1e7
1e8
1
10
100
1e3
1e4
Frequency Hz
1e5
1e6
1e7
1e8
dB(Vout.v)
40
20
0
phase(Vout.v) Degrees
400
200
0
Figure 2: Gain and phase curves for a basic OP AMP inverting amplifier.
3
T6
P_VCC
T7
T14
T15
T24
T27
R10
R=50
T3
R5
R=39k
VIN_N
T4
T18
C1
C=30pF
VIN_P
T21
VOUT
R11
R=25
T26
T2
T5
R9
R=40k
T17
T23
T13
T11
T12
T8
T10
T19
T16
R1
R=3k
R4
R=1k
R3
R=50k
R6
R=50k
R2
R=1k
R7
R=50
R8
R=50k
T20
P_VEE
Figure 3: Transistor level circuit for the UA741 operational amplifier.
4
Vout.v
10
5
0
1
10
100
1e3
1e4
Frequency Hz
1
10
100
1e3
1e5
1e6
1e7
dB(Vout.v)
20
0
-20
1e4
1e5
1e6
1e7
1e3
1e4
Frequency Hz
1e5
1e6
1e7
Frequency Hz
phas(Vout.v)
200
100
0
1
10
100
Figure 4: Gain and phase curves for a times 10 inverting amplifier with the OP
AMP represented by a transistor level UA741 model.
R2
R=47k Ohm
Vin
V1
U=1 V R3
R=4.7k Ohm
R1
R=200k Ohm
Vout
C1
C=159.15nF
OP1
G=1
SRC1
G=1 S
T=0
dc simulation
ac simulation
DC1
AC1
Type=lin
Start=1 Hz
Stop=10 MHz
Points=1800
Equation
Eqn1
d2=phase(Vout.v)
d1=dB(Vout.v)
Figure 5: Modified Qucs OP AMP model to include single pole frequency response.
5
Vout.v
10
5
0
1
10
100
1e3
1e4
1e5
1e6
1e7
1e4
1e5
1e6
1e7
Frequency Hz
dB(Vout.v)
20
0
-20
1
10
100
1e3
Frequency Hz
phase(Vout.v) Degrees
200
150
100
1
10
100
1e3
1e4
1e5
1e6
Frequency Hz
Figure 6: Gain and phase curves for the circuit shown in Fig. 5.
6
1e7
Adding features to the Qucs OP AMP model
In the previous section it was shown that the Qucs OP AMP model had a frequency
response that is independent of frequency. By adding external components to the
Qucs OP AMP model the functionality of the model can be improved. The UA741
differential open loop gain has a pole at roughly 5Hz and a frequency response
that decreases at 20 dB per frequency decade from the first pole frequency up to
a second pole frequency at roughly 3 MHz. The circuit shown in Fig. 5 models
the differential frequency characteristics of a UA741 from DC to around 1 MHz.
Figure 6 illustrates the closed loop frequency response for the modified Qucs OP
AMP model.
Modular operational amplifier macromodels
Macromodelling is a term given to the process of modelling an electronic device
as a ”black box” where individual device characteristics are specified in terms of
the signals, and other properties, observed at the input and output terminals
of the black box. Such models operate at a functional level rather than at the
more detailed transistor circuit level, offering considerable gain in computational
efficiency.2 Macromodels are normally derived directly from manufacturers data
sheets. For the majority of operational amplifiers, transistor level models are not
normally provided by manufacturers. One notable exception being the UA741 operational amplifier shown in Fig. 3.
A block diagram of a modular3 general purpose OP AMP macromodel is illustrated
in Fig. 7. In this diagram the blocks represent specific amplifier characteristics
modelled by electrical networks composed of components found in all the popular
circuit simulators4 . Each block consists of one or more components which model a
single amplifier parameter or a group of related parameters such as the input offset
current and voltage. This ensures that changes to one particular parameter do not
indirectly change other parameters. Local nodes and scaling are also employed
in the macromodel blocks. Furthermore, because each block operates separately,
2
Computational efficiency is increased mainly due to the fact that operational amplifier
macromodels have, on average, about one sixth of the number of nodes and branches when
compared to a transistor level model. Furthermore, the number of non-linear p-n junctions
included in a macromodel is often less than ten which compares favorable with the forty to fifty
needed to model an amplifier at transistor level.
3
Brinson M. E. and Faulkner D. J., Modular SPICE macromodel for operational amplifiers,
IEE Proc.-Circuits Devices Syst., Vol. 141, No. 5, October 1994, pp. 417-420.
4
Models employing non-linear controlled sources, for example the SPICE B voltage and current sources, are not allowed in Qucs release 0.0.9. Non-linear controlled sources are one of the
features on the Qucs to-do list.
7
scaled voltages do not propagate outside individual blocks. Each block can be
modelled with a Qucs subcircuit that has the required specification and buffering
from other blocks. Moreover, all subcircuits are self contained entities where the
internal circuit details are hidden from other blocks. Such an approach is similar to structured high-level computer programming where the internal details of
functions are hidden from users. Since the device characteristics specified by each
block are separate from all other device characteristics only those amplifier characteristics which are needed are included in a given macromodel. This approach
leads to a genuinely structured macromodel. The following sections present the
detail and derivation of the electrical networks forming the blocks drawn in Fig. 7.
To illustrate the operation of the modular OP AMP macromodel the values of the
block parameters are calculated for the UA741 OP AMP and used in a series of
example simulations. Towards the end of this tutorial note data are presented for
a number of other popular general purpose operational amplifiers.
A basic AC OP AMP macromodel.
A minimum set of blocks is required for the modular macromodel to function as
an amplifier: an input stage, a gain stage and an output stage. These form the
core modules of all macromodels.
The input stage.
The input stage includes amplifier offset voltage, bias and offset currents, and the
differential input impedance components. The circuit for the input stage is shown
in Fig. 8, where
1. R1 = R2 = Half of the amplifier differential input resistance (RD).
2. Cin = The amplifier differential input capacitance (CD).
3. Ib1 = Ib2 = The amplifier input bias current (IB ).
4. Ioff = Half the amplifier input offset current (IOFF ).
5. Voff1 = Voff2 = Half the input offset voltage ( VOFF ).
Typical values for the UA741 OP AMP are:
1. RD = 2 MΩ and R1 = R2 = 1MΩ
2. CD = Cin1 = 1.4 pF.
8
3. IB = Ib1 = Ib2 = 80 nA.
4. IOFF = 20 nA and Ioff1 = 10 nA.
5. VOFF = 0.7 mV and Voff1 = Voff2 = 0.35 mV.
9
In+
Common
mode stage
In-
Input Stage
Signal
adder
Slew rate
limiting stage
Voltage gain
stage 1
Overdrive limiting
stage
Vcc
In+
Out
Voltage gain
stage 2
InVee
Output stage
RPD
Vee
Vcc
Vcc
Vee
Current limiting
stage
Voltage limiting
stage
Figure 7: Block diagram of an operational amplifier macromodel.
10
The differential output signal (VD) is given by V D− P 1−V D− N 1 and the common
mode output signal (VCM ) by (V D− P 1 + V D− N 1)/2.
Voff1
U=0.35mV
Ib1
I=80nA
IN_N1
R1
R=1M Ohm
VCM1
Ioff1
I=10nA
Voff2
U=0.35mV
Ib2
I=80nA
VD_N1
Cin1
C=1.4 pF
R2
R=1M Ohm
IN_P1
Vcm
In+
VD_P1
Figure 8: Modular OP AMP input stage block.
11
Input
stage
InVd-
Vd+
SUB1
File=input_stage.sch
Voltage gain stage 1.
The circuit for voltage gain stage 1 is shown in Fig. 9, where
1. RD1 = 100 MΩ = A dummy input resistor - added to ensure nodes IN− P 1
and IN− N 1 are connected by a DC path.
2. GMP1 = 1 S = Unity gain voltage controlled current generator.
3. RADO = The DC open loop differential gain ( AOL(DC) ) of the OP AMP.
4. CP1 = 1/(2*π*GBP), where GBP = the OP AMP gain bandwidth product.
Typical values for the UA741 OP AMP are:
1. RADO = 200kΩ. (AOL(DC) = 106 dB)
2. CP1 = 159.15 nF (The typical value for UA741 GBP is 1 MHz).
Derivation of voltage gain stage 1 transfer function
Most general purpose operational amplifiers have an open loop differential voltage
gain which has (1) a very high value at DC (2) a dominant pole (fp1 ) at a low
frequency - typically below 100 Hz, and (3) a gain response characteristic that
rolls-off at 20 dB per decade up to a unity gain frequency which is often in the
MHz region. This form of response has a constant gain bandwidth product (GBP )
over the frequency range from fp1 to GBP. A typical OP AMP differential open
loop response is shown in Fig. 10. The voltage gain transfer function for this type
of characteristic can be modelled with the electrical network given in Fig. 9, where
the the AC voltage transfer function is
vout(P OLE− 1− OU T 1) =
GM P 1 ∗ (V (IN− P 1) − V (IN− N 1)) ∗ RADO
1 + j(ω ∗ RADO ∗ CP 1)
(1)
POLE1
IN+
IN_P1
IN_N1
RD1
R=100M
RADC1
R=200k Ohm
CP1
C=159.15 nF
POLE_1_OUT1
GMP1
G=1 S
T=0
OUT
INSUB1
File=pole1.sch
Figure 9: Modular OP AMP first voltage gain stage.
12
Aol
Aol(DC)
1
fp1
GBP
f Hz
Figure 10: OP AMP open loop differential voltage gain as a function of frequency.
Where
1
(2)
2π ∗ RADO ∗ CP 1
Let RADC = Aol(DC) and GMP1 = 1 S. Then, because fp1*AOL(DC) = GBP,
fP 1 =
CP 1 =
1
2π ∗ GBP
13
(3)
OUTSTG_OUT1
IN_P1
RD1
R=100M
ROS1
R=75 Ohm
EOS1
G=1
T=0
IN_N1
Output
stage
In+
Out
InSUB1
File=out_stage.sch
Figure 11: Modular macromodel output stage.
Output stage.
The electrical network representing a basic output stage is given in Fig. 11, where
1. RD1 = 100 MΩ = A dummy input resistor - added to ensure nodes IN− P 1
and IN− N 1 are connected by a DC path.
2. EOS1 G = 1 = Unity gain voltage controlled voltage generator.
3. ROS1 = OP AMP output resistance.
A typical value for the UA741 OP AMP output resistance is ROS1 = 75Ω.
A subcircuit model for the basic AC OP AMP macromodel
The model for the basic AC OP AMP macromodel is shown in Fig. 12. The input stage common mode voltage (V cm) is not used in this macromodel and has
been left floating. To test the performance of the AC macromodel it’s operation
was compared to the transistor level UA741 model. Figure 13 shows a schematic
circuit for two inverting amplifiers, each with a gain of ten, driven from a common AC source. One of the amplifiers uses the simple AC macromodel and the
other the transistor level UA741 model. Figure 14 illustrates the output gain and
phase curves for both amplifiers. In general the plotted curves are very similar.
However, at frequencies above the GBP frequency the basic AC macromodel does
not correctly model actual OP AMP performance. This is to be expected because
the simple AC macromodel does not include any high frequency modelling components. Notice also that the DC output voltages for vout and vout3 are very
similar, see the DC tabular results given in Fig. 13.
14
SUB2
File=input_stage.sch
In+
Vd+
IN_P1
POLE1
IN+
Vcm
OUT
Output
stage
In+
ININ_N1
In- VdInput
stage
SUB4
File=pole1.sch
InOUT1
OP AMP
IP1O
Out
In-
In+
SUB3
File=out_stage.sch
SUB5
File=op_amp_ac_IP1O.sch
Figure 12: Simple AC OP AMP macromodel.
15
dc simulation
ac simulation
DC1
AC1
Type=lin
Start=1 Hz
Stop=10 MHz
Points=1801
number
1
vout.V
0.0068
vout3.V
0.0069
Equation
Eqn1
yp=phase(vout.v)
yp3=phase(vout3.v)
ydb=dB(vout.v)
ydb3=dB(vout3.v)
R1
R=10k Ohm
vin
Invout
V1
R2
U=1 V R=1k Ohm
OP AMP
IP1O
SUB5
In+
R3
R=10k Ohm
SUB6
R8
R=1k Ohm
vout3
VEE
UA741_tran
V2
U=15 V
VCC
+
V3
U=15 V
Figure 13: Test circuit for an inverting amplifier. Output signals: (1) vout for AC
macromodel, (2) vout3 for UA741 transistor model.
16
200
phase(vout.v) in degrees
dB(vout.v)
20
0
-20
1
10
100
1e3 1e4 1e5
Frequency Hz
1e6
100
1e7
1
10
100
1e3 1e4 1e5
Frequency Hz
1e6
1e7
1
10
100
1e3 1e4 1e5
Frequency Hz
1e6
1e7
200
phase(vout3.v) in degrees
20
db(vout3.v)
150
0
-20
1
10
100
1e3 1e4 1e5
Frequency Hz
1e6
100
0
1e7
Figure 14: Simulation test results for the circuit shown in Fig. 13.
17
A more accurate OP AMP AC macromodel
Most general purpose OP AMPs have a high frequency pole in their differential
open loop gain characteristics. By adding a second gain stage to the simple AC
macromodel the discrepancy in the high frequency response can be corrected. The
model for the second gain stage is shown in Fig. 15. This additional gain stage
has a structure similar to the first gain stage, where
1. RD2 = 100 MΩ = A dummy input resistor - added to ensure nodes IN_P2
and IN_N2 are connected by a DC path.
2. GMP2 = 1 S = Unity gain voltage controlled current generator.
3. RP2 = 1Ω.
4. CP2 = 1/(2π*fp2), where f p2 = the second pole frequency in Hz.
A typical value for the UA741 OP AMP high frequency pole is fp2 = 3M Hz
Derivation of voltage gain stage 2 transfer function.
The differential voltage gain transfer function for voltage gain stage 2 is given by
vout(P OLE− 2− OU T 1) =
GM P 2 ∗ (V (IN− P 2) − V (IN− N 2)) ∗ RP 2
1 + j(ω ∗ RP 2 ∗ CP 2)
(4)
Let RP2 = 1Ω and GMP2 = 1 S. Then
vout(P OLE− 2− OU T 1) =
V (IN− P 2) − V (IN− N 2)
1 + j(ω ∗ CP 2)
(5)
and
CP 2 =
1
2π ∗ f p2
(6)
POLE2
IN+
IN_P2
IN_N2
RD2
R=100M
RP2
R=1 Ohm
GMP2
G=1 S
T=0
CP2
C=53.05nF
POLE_2_OUT1
OUT
INSUB1
File=pole2.sch
Figure 15: Modular OP AMP second voltage gain stage.
18
ac simulation
AC1
Type=log
Start=1 Hz
Stop=100MHz
Points=241
R1
R=10M Ohm
In-
C1
C=100mF
vout
vin
OP AMP
IP1P2O
In+
V1
U=1 V
SUB1
File=op_amp_ac_IP1P2O.sch
SUB2
C2
C=100 mF
R2
R=10M Ohm
Equation
Eqn1
y4=rad2deg(unwrap(angle(vout3.v)))
y=dB(vout.v)
y3=dB(vout3.v)
y2=phase(vout.v)
dc simulation
DC1
V2
U=15 V
VEE
vout3
UA741_tran
VCC
V3
U=15 V
+
Figure 16: Test circuit for simulating OP AMP open loop differential gain.
Simulating OP AMP open loop differential gain
The circuit shown in Fig. 16 allows the open loop differential gain (Aol(f )) to
be simulated. This circuit employes a feedback resistor to ensure DC stability.
Fig. 16 illustrates two test circuits driven from a common AC source. This allows
the performance of the AC macromodel and the UA741 transistor level model to
be compared. The AC voltage transfer function for the test circuit is
vout(f ) =
Aol(f )
vin(f )
Aol(f )
1+
1 + jω ∗ R ∗ C
where vout(f ) = (V + − V − ) ∗ Aol(f ), V + = vin(f ), and V − =
(7)
vout(f )
1 + jω ∗ R ∗ C
Aol(f )
<< 1, equation (7) becomes vout(f ) ⇒ Aol(f ) ∗ vin(f ).
ω∗R∗C
Hence, for those frequencies where this condition applies vout(f ) = Aol(f ) when
vin(f ) = 1 V. Figure 17 shows plots of the open loop simulation data. Clearly with
the test circuit time constant set at 1e6 seconds the data is accurate for frequencies
down to 1 Hz.
Provided
19
1e5
1e4
1e3
vout3.v
vout.v
1e5
1e4
1e3
100
10
1
0.1
0.01
1e-3
1e-4
100
10
1
1
10
0.1
0.03
100 1e3 1e4 1e5 1e6 1e7 1e8
Frequency Hz
phase(vout.v) degrees
dB(vout3.v)
1
10
100 1e3 1e4 1e5 1e6 1e7 1e8
Frequency Hz
1
10
100 1e3 1e4 1e5 1e6 1e7 1e8
Frequency Hz
0
-100
1
10
1
10
100 1e3 1e4 1e5 1e6 1e7 1e8
Frequency Hz
0
100 1e3 1e4 1e5 1e6 1e7 1e8
Frequency Hz
phase(vout3.v) degrees
dB(vout.v)
0
-200
10
100
100
-100
1
100 1e3 1e4 1e5 1e6 1e7 1e8
Frequency Hz
0
-200
Figure 17: Simulation test results for the circuit shown in Fig. 16.
20
Adding common mode effects to the OP AMP AC
macromodel
The open-loop differential gain AD (f ) for most general purpose operational amplifiers can be approximated by
1
AD (f ) = AD(0)
1+j
(8)
f
fP D
Similarly, the common-mode gain ACM (f ) can be represented by the same singlepole response and a single zero response given by
1+j
ACM (f ) = ACM (0)
f
fCM Z
f
1+j
fP D
(9)
Defining the common-mode rejection ratio CM RR(f ) of an OP AMP as
CM RR(f ) =
AD (f )
ACM (f )
(10)
gives
1
CM RR(f ) = CM RR(0)
1+j
where
CM RR(0) =
f
(11)
fCM Z
AD (0)
ACM (0)
(12)
Common-mode effects can be added to OP AMP macromodels by including a
stage in the modular macromodel that introduces a zero in the amplifier frequency
response. Output VCM from the macromodel input stage senses an amplifier common mode signal. This signal, when passed through a CR network generates the
required common mode zero. Figure 18 gives the model of the zero generating
network, where.
1. RDCMZ = 650 MΩ = common-mode input resistance/2.
2. RCM1 = 1 MΩ
RCM 1
3. ECM1 G = 31.623 = RCM 2 . (NOTE: RCM1/RCM2 is a scaling factor.)
CM RR(0)
21
IN_P1
IN_N1
CMV_OUT1
RCM1
R=1M
RDCMZ
R=650M
ECM1
G=31.623
T=0
RCM2
R=1
CMZERO
IN+
CCM1
C=795.8 pF
OUT
INSUB1
File=cmzero.sch
Figure 18: Common-mode zero macromodel
4. CCM1 = 795.8 pF =
1
.
2π ∗ RCM 1 ∗ fCM Z
5. RCM2 = 1 Ω
Typical values for the UA741 OP AMP are:
1. Common-mode input resistance = 1300 MΩ.
2. CMRR(0) = 90 dB
3. fCM Z = 200 Hz.
The AC voltage transfer function for the common-mode zero transfer function is
RCM 2 1 + jω ∗ RCM 1 ∗ CCM 1
[V (IN_P1) − V (IN_N1)]
V out(CMV_OUT1) = G(ECM 1)
RCM 1 1 + jω ∗ RCM 2 ∗ CCM 1
(13)
RCM 2
As
<< 1, the pole introduced by the common-mode RC network is at a
RCM 1
very high frequency and can be neglected. Combining the common-mode zero with
the previously defined stage models yields the macromodel shown in Fig. 19. In
this model the differential and common-mode signals are combined using a simple
analogue adder based on voltage conrolled current generators.
Simulating OP AMP common-mode effects
OP AMP common-mode effects can be simulated using the circuit shown in Fig. 20.5
The resulting output voltages (vout.v and vout3.v) for a test circuit with matched
5
Brinson M.E. and Faulkner D.J., New approaches to measurement of operational amplifier
common-mode rejection ratio in the frequency domain, IEE Proc-Circuits Devices Sys., Vol 142,
NO. 4, August 1995, pp 247-253.
22
SUB6
In+
VSUM
IN1+
Vd+
IN_N1
POLE1
IN1-
Vcm
IN+
OUT
IN2+
InIN_P1
VdInput
stage
SUB5
CMZERO
IN+
SUB4
OUT
Output
stage
In+
IN-
Out
In-
SUB3
SUB2
In-
INSUB1
File=cmzero.sch
IN+
IN-
IN2-
OUT
POLE2
OUT
OP_AMP
ICMZP1P2O
In+
SUB7
File=op_amp_ac_ICMZP1P2O.sch
WHERE
VSUM
IN1+
IN1-
RSUM1
R=1
IN1_P1
IN1_N1
OUT
SUM_OUT1
GMSUM1
G=1 S
T=0
IN2+
IN2-
SUB8
File=VSUM.sch
IN2_P1
IN2_N1
GMSUM2
G=1 S
T=0
Figure 19: AC macromodel including common-mode zero.
23
OUT1
R1
R=10k
dc simulation
In-
vin
DC1
ac simulation
AC1
Type=log
Start=1 Hz
Stop=10 kHz
Points=401
V1
U=1 V
R2
R=10k
vout
OP_AMP
ICMZP1P2O
In+
R3
R=10k
SUB1
R4File=op_amp_ac_ICMZP1P2O.sch
R=10k
R6
SUB2 R=10k
File=ua742_tran.sch
R5
R=10k
VEE
vout3
UA741_tran
VCC
+
R7
R=10k
V2
U=15 V
V3
U=15 V
R8
R=10k
Figure 20: Simulation of OP AMP common-mode performance.
vout(0)
1
=
. Clearly the
vin
CM RR(0)
test results for the macromodel and the UA741 transistor model are very similar.
In the case of the macromodel typical device parameters were used to calculate the
macromodel component values. However, in the transistor level model the exact
values of the component parameters are unknown.6
resistors are shown plotted in Fig. 21, where
6
The UA741 transistor level model is based on an estimate of the process parameters that
determine the UA741 transistor characteristics. Hence, the device level model is unlikely to be
absolutely identical to the model derived from typical parameters values found on OP AMP data
sheets. From the simulation results the CMRR(0) values are approximately (1) macromodel
90 dB, (2) UA741 transistor model 101 dB. Similarly, the common-mode zero frequencies are
approximately (1) macromodel 200 Hz, (2) UA741 transistor model 500 Hz.
24
vout.v
1e-3
1e-4
3e-5
1
10
100
Frequency Hz
1
10
100
Frequency Hz
1e3
1e4
vout3.v
1e-4
1e-5
3e-6
1e3
Figure 21: Simulation test results for the circuit shown in Fig. 20.
25
1e4
Large signal transient domain OP AMP macromodels
The modular macromodel introduced in the previous sections concentrated on
modelling OP AMP performance in the small signal AC domain. Large signal
models need to take into account the passage of signals through an OP AMP in
the time domain and limit the excursion of voltage and current swings to the practical values found in actual amplifiers. Starting with the AC domain macromodel
introduced in the previous sections, adding a slew rate limiting stage and a overdrive stage will more correctly model OP AMP high speed large signal limitations.
Furthermore, by adding output voltage and current limiting stages the OP AMP
macromodel will correctly model large signal effects when signal levels approach
circuit power supply voltages or the OP AMP output current limits.
Slew rate macromodel derivation
The slew rate of an OP AMP can be modelled by limiting the current charging
CP 1 in the first voltage gain stage POLE1. From Fig. 9
GM P 1 (V (IN− P 1) − V (IN− N 1)) =
dV (P OLE− 1− OU T 1)
V (P OLE− 1− OU T 1)
+CP 1∗
RADO
dt
(14)
Hence, provided RADO is large7
GM P 1 (V (IN− P 1) − V (IN− N 1)) ' CP 1 ∗
dV (P OLE− 1− OU T 1)
dt
(15)
1
But CP 1 =
2π ∗ GBP
Yielding
GM P 1 (V (IN− P 1) − V (IN− N 1)) '
Moreover, if
current
1
dV (P OLE− 1− OU T 1)
∗
2π ∗ GBP
dt
(16)
dV (P OLE− 1− OU T 1)
is set equal to the OP-AMP slew rate then the
dt
charging CP1 will be limited to the maximum allowed. In Fig. 9 GM P 1 is 1 S.
7
This condition is normally true because RADO is set to the DC open loop differential gain
in macromodule POLE1.
26
GMSRT1
G=0.01 S
T=0
D1
RSCALE1
R=100 Ohm
IN_P1
IN_N1
VSR1
U=7.26 V
SLEWRT
RSRT1
SLEWRT_OUT1
R=1
IN+
OUT
IN-
SRC1
G=1 S
T=0
SUB1
File=slewrt.sch
Figure 22: OP AMP slew rate macromodel.
Therefore, voltage difference V (IN− P 1) − V (IN− N 1)
must be set to
1
dV (P OLE− 1− OU T 1)
∗
.
2π ∗ GBP
dt
This is done by the network SLEWRT shown in Fig. 22, where
1. RSCALE1 = 100 Ω = Scaling resistance (Scale factor x 100).
2. SRC1 G = 1 S.
3. VSR1 = V1.
4. GMSRT1 G = 0.01 S. (Scale factor = 1/100).
5. RSRT1 = 1 Ω
And,
1. V 1 =
100 ∗ P ositive− slew− rate
− 0.7V
2π ∗ GBP
2. V 2 =
100 ∗ N egative− slew− rate
− 0.7V
2π ∗ GBP
3. The diode parameters are IS=1e-12 IBV=20mA BV=V1+V2, others default.
Typical values for the UA741 OP AMP are:
1. P ositive− slew− rate = N egative− slew− rate = 0.5V/µS.
2. V 1 = V 2 = 7.25V.
Scaling is used in the slew rate model to allow the use of higher voltages in
the clamping circuit. Increased voltages reduce errors due to the forward biased
junction voltage. Current limiting results by clamping the voltage across resistor
RSCALE1 with a diode. This diode acts as a zener diode and saves one nonlinear
junction when compared to conventional clamping circuits. The output section of
27
the SLEWRT circuit removes the internal scaling yielding an overall gain of unity
for the module.
The circuit in Fig. 23 demonstrates the effect of slew rate limiting on OP AMP
transient performance. Three identical OP AMP inverter circuits are driven from
a common input 10 kHz AC signal source. Voltage controlled voltage sources are
used to amplify the input signal to the second and third circuits. The three input
signals are (1) 5 V peak, (2) 10 V peak and (3) 15 V peak respectively. The input
and output waveforms for this circuit are illustrated in Fig. 24. The effect of slew
rate limiting on large signal transient performance is clearly demonstrated by these
curves. In the case of the 15 V peak input signal the output signal (vout3.Vt) has
a slope that is roughly 0.5 V per µS.
Modelling OP AMP overdrive and output voltage limiting
Large transient signals can overdrive an OP AMP causing it’s output voltage to
saturate. On removal of the overdrive signal an OP AMP takes a finite time to
recover8 and return to normal linear circuit behaviour. When saturated the output
voltage is clamped at a voltage close to the plus or minus power rail voltage. The
overdrive and voltage clamping properties of an OP AMP are related and macromodels for both effects need to be added to an OP AMP model when simulating
OP AMP overdrive characteristics. However, in many circuit simulations the overdrive macromodel can be left out without loss of functionality or accuracy.
The effect of overdrive signals can be modelled by a voltage clamping circuit which
takes account of OP AMP recovery time from voltage overdrive. This extra element
clamps the output of the POLE1 module at a level above the OP AMP DC supply
voltages. The overall effect of the overdrive circuit is to delay the restoration of
linear circuit behaviour when an overload signal is removed. In contrast to the
overdrive module the output voltage limiting module clamps the output voltage to
a voltage close to the power rail voltages, clipping any output voltage excursions
above the power rail voltage levels. Figure 25 illustrates the macromodels for the
overdrive and output voltage limiting models, where
1. VOVDR1 = 2.5 V = (Positive slew rate)*(Amplifier recovery time).
2. VOVDR2 = 2.5 V = (Negative slew rate)*(Amplifier recovery time).
3. VLIM1 = 2.0 V = (+ supply voltage) - (Maximum positive output voltage)
+ 1 V.
8
Overload recovery time of an OP AMP is the time required for the output voltage to recover
to a rated output voltage from a saturated condition. Typical values are in the µ S region.
28
transient
simulation
In-
vin
In+
V1
U=5 V
OP_AMP
ICMZ
SLEWRT
P1P2O
TR1
Type=lin
Start=0
Stop=200us
vout1
SUB1
File=op_amp_ac_ICMZP1P2O.sch
In-
In+
OP_AMP
ICMZ
SLEWRT
P1P2O
vout2
SUB2
File=op_amp_ac_ICMZP1P2O.sch
SRC1
G=2
T=0
In-
In+
OP_AMP
ICMZ
SLEWRT
P1P2O
SUB3
File=op_amp_ac_ICMZP1P2O.sch
SRC2
G=3
T=0
Figure 23: OP AMP slew rate test circuit.
29
vout3
vin.Vt
5
0
-5
0
2e-5
4e-5
6e-5
8e-5
1e-4
time
1.2e-4
1.4e-4
1.6e-4
1.8e-4
2e-4
0
2e-5
4e-5
6e-5
8e-5
1e-4
time
1.2e-4
1.4e-4
1.6e-4
1.8e-4
2e-4
vout1.Vt
5
0
-5
vout2.Vt
10
0
-10
0
2e-5
4e-5
6e-5
8e-5
1e-4
time
1.2e-4
1.4e-4
1.6e-4
1.8e-4
2e-4
0
2e-5
4e-5
6e-5
8e-5
1e-4
time
1.2e-4
1.4e-4
1.6e-4
1.8e-4
2e-4
20
vout3.Vt
10
0
-10
Figure 24: OP AMP slew rate simulation waveforms for the circuit shown in
Fig. 23.
30
P_VCC1
P_VCC2
VOVDRV1
U=2.5 V
VLIM1
U=2 V
DOVRV1
Is=8e-16 A
VCC
OVDRV SUB1
File=OVDRV.sch
IN
P_IN1
DOVDRV1
Is=8e-16 A
VEE
P_IN2
DVL1
Is=8e-16 A
VCC
SUB2
IN VLIMIT File=vlimit.sch
DVL2
Is=8e-16 A
VEE
VLIM2
U=2 V
VOVDRV2
U=2.5 V
P_VEE2
P_VEE1
Figure 25: OP AMP overdrive and output voltage limiting macromodels.
4. VLIM2 = 2.0 V = (- supply voltage) - (Maximum negative output voltage)
+ 1 V.
5. The diode parameters are Is = 8e-16 A, others default.
Typical values for the UA741 OP AMP are:
1. Amplifier recovery time 5 µS.
2. + supply voltage = 15 V.
3. - supply voltage = -15 V.
4. Maximum positive output voltage = 14 V.
5. Maximum negative output voltage = -14 V.
The test circuit given in Fig. 26 illustrates the effects of signal overdrive and output
voltage clamping on a unity gain buffer circuit. The test input signal is a 1 kHz
signal with the following drive voltages (1) vin1 = 10 V peak, (2) vin2 = 18 V
peak, and (3) vin3 = 22 V peak. The corresponding output waveforms are shown
in Fig. 27. These indicate that increasing overdrive signals results in longer OP
AMP recovery times before the amplifier returns to linear behaviour.
Modelling OP AMP output current limiting
Most general purpose OP AMPs have a network at the circuit output to protect
the device from high load currents generated by shorting the output terminal to
ground or some other situation where a high current flows through the OP AMP
31
V2
U=15 V
In-
vin1
V1
U=10 V
VCC
vout1
OP_AMP
ICMZ
SLEWRT OVDRV
P1P2O
In+
VEE
SUB1
V3
U=15 V
transient
simulation
TR1
Type=lin
Start=0
Stop=1.20 ms
In-
vin2
VCC
vout2
OP_AMP
ICMZ
SLEWRT OVDRV
P1P2O
In+
VEE
dc simulation
DC1
SUB2
SRC1
G=1.8
T=0
In-
vin3
VCC
vout3
OP_AMP
ICMZ
SLEWRT OVDRV
P1P2O
In+
VEE
SUB3
SRC2
G=2.2
T=0
Figure 26: OP AMP overdrive and output voltage limiting test circuit.
32
vout1.Vt
vin1.Vt
10
0
-10
0
1e-4
2e-4
3e-4
4e-4
5e-4
6e-4
Time
7e-4
8e-4
9e-4
1e-3
0.0011
0.0012
0
1e-4
2e-4
3e-4
4e-4
5e-4
6e-4
Time
7e-4
8e-4
9e-4
1e-3
0.0011
0.0012
0
1e-4
2e-4
3e-4
4e-4
5e-4
6e-4
Time
vout2.Vt
vin2.Vt
20
0
-20
vout3.Vt
vin3.Vt
20
0
-20
7e-4
8e-4
9e-4
1e-3
0.0011
0.0012
Figure 27: OP AMP overdrive and output voltage limiting waveforms for the
circuit shown in Fig. 26.
33
D2
Is=1e-15 A
D1
Is=1e-15 A
P_OUT1
CLIMIT
IN
OUT
P_IN1
RDCL1
R=100M
HCL1
G=36
T=0
SUB1
File=CLIMIT.sch
ECL1
G=1
T=0
Figure 28: OP AMP output current limiter macromodel.
output stage. The electrical network shown in Fig. 28 acts as a current limiter:
current flowing between pins P_IN1 and P_OUT1 is sensed by current controlled
voltage generator HCL1. The voltage output from generator HCL1 is in series
with voltage controlled generator ECL1. The connection of these generators is in
opposite polarity. Hence, when the load current reaches the maximum allowed by
the OP AMP either diode DCL1 or DCL2 turns on clamping the OP AMP output
voltage preventing the output current from increasing. The parameters for the
current limiter macromodel are given by
1. RDCL1 = 100 MΩ = Dummy resistor.
2. ECL1 G = 1.
3. HCL1 G = 36Ω = 0.9 V/(Maximum output current A).
4. The diode parameters are Is = 1e-15 A, others default.
A typical value for the UA741 OP AMP short circuit current is 34 mA at 25o C.
Figures 29 and 30 show a simple current limiter test circuit and the resulting test
waveforms. In this test circuit time controlled switches decrease the load resistors
at 1 mS intervals. When the load current reaches roughly 34 mA the output
voltage is clamped preventing further increases in load current.
34
V2
U=15 V
In-
VCC
OP_AMP
ICMZ
SLEWRT OVDRV
P1P2O CLIMIT
vin
In+
V1
U=10 V
vout
VEE
SUB1
S1
V3
U=15 V
R1
R=1k
dc simulation
R2
R=1k
S2
R3
R=2k
S3
S4
R4
R=2k
R5
R=2k
S5
R6
R=2k
transient
simulation
DC1
TR1
Type=lin
Start=0
Stop=8 ms
Figure 29: OP AMP output current limiter test circuit.
vin.Vt
10
0
-10
0
5e-4
1e-3
0.0015
0.002
0.0025
0.003
0.0035
0.004
Time
0.0045
0.005
0.0055
0.006
0.0065
0.007
0.0075
0.008
0
5e-4
1e-3
0.0015
0.002
0.0025
0.003
0.0035
0.004
Time
0.0045
0.005
0.0055
0.006
0.0065
0.007
0.0075
0.008
vout.Vt
10
0
-10
Figure 30: Simulation waveforms for current limiter test circuit shown in Fig. 29.
35
Parameter
Offset voltage (V)
Bias current (A)
Offset current (A)
Differential input res. (ohm)
Differential input cap. (F)
Avd(0) dB
fp1 (Hz)
fp2 (Hz)
CMRR(0) dB
fcm (Hz)
GBP (Hz)
Rout (ohm)
Slew rate (V per micro sec.)
Overdrive recovery time (S)
DC supply current (A)
Short circuit output current(A)
Common-mode input res. (ohm)
Common-mode input cap. (F)
UA741
7e-4
80e-9
20e-9
2e6
1.4e-12
106
5
3e6
90
200
1e6
75
0.5
5e-6
1.4e-3
34e-3
1.3e8
OP27
30e-6
15e-9
12e-9
4e6
OP42
4e-4
130e-12
6e-12
1e12
6e-12
125
120
6
20
17e6
20e6
125
96
2e3
100e3
8e6
10e6
70
50
2.8
50
700e-9
2.5e-3 5.1e-3
32e-3 30e-3
2e9
OPA134
5e-4
5e-12
2e-12
1e13
2e-12
120
5
10e6
100
500
8e6
10
20
0.5e-6
4e-3
40e-3
1e13
5e-12
AD746
3e-4
110e-12
45e-12
2e11
5.5e-12
109
0.25
35e6
85
3e3
13e6
10
75
AD826
5e-4
3-3e-6
25e-9
300e3
1.5e-12
75
10e3
100e6
100
2e3
35e6
8
300
7e-3
25e-3
2.5e11
5.5e-12
6.6e-3
90e-3
Table 1: Typical OP AMP parameters taken from device data sheets.
36
Obtaining OP AMP macromodel parameters from
published device data
The OP AMP modular macromodel has one very distinct advantage when compared to other amplifier models namely that it is possible to derive the macromodel
parameters directly from a common set characteristics found on the majority of
manufacturer’s data sheets. The data given in Table. 1 shows a typical range of
values found on OP AMP data sheets. In cases where a particular parameter is
not given then a starting point is to use a value obtained from a data sheet of an
equivalent device. The macromodel element values are then calculated using the
equations presented in the previous sections of this tutorial. As a rule of thumb it is
good practice to test each block in the modular macromodel prior to constructing
a complete OP AMP macromodel.
More complete design examples.
In this section two larger design examples are presented. These demonstrate the
characteristics of the various OP AMP macromodels introduced in the previous
text and attempt to give readers guidance as to the correct model to choose for a
particular simulation.
Example 1: State variable filter design and simulation
The circuit given in Fig. 31 is a state variable filter which simultaneously generates
band-pass, high-pass and low-pass responses. The circuit consists of an OP AMP
adder and two integrator circuits and requires three OP AMPS, two capacitors
and a number of resistors. The selection of the type of OP AMP for successful
operation of this filter is critical because devices with high offset voltage will cause
the integrators to saturate and the circuit will not function correctly. For operation
below 20 kHz the OP27 is a good choice of OP AMP because of it’s low offset
voltage in the µV region. In this simulation both the DC characteristics and small
signal AC transfer characteristics are needed to check the filter design, hence the
AC macromodel with the DC parameters embedded in the input stage should allow
accurate modelling of the filter performance.9 The insert in Fig. 31 list the DC
output voltages for each of the OP AMP stages indicating that the integrators are
not saturated. The design of the state variable filter uses the following equations:
9
The magnitude of the output signals from the filter should also be checked to ensure that
these signals do not exceed the power supply voltages.
37
1. The superposition principle yields
R1
R1
R4
R1
vlp + 1 +
vbp
vhp = − vin −
R6
R7
R7 k R6 R4 + R5
(17)
When R1 = R6 = R7
3R4
vbp
R4 + R5
(18)
vhp
(19)
vhp = −vin − vlp +
2. Also
vbp = −
where
f0 =
1
j ff0
1
1
=
2πR2 C1
2πR3 C2
(20)
3. Similarly
vlp = −
4. Hence
Where
1
j ff0
vbp = −
vhp
(21)
( ff0 )2
vhp
=
vin
1 − ( ff0 )2 + ( Qj )( ff0 )
(22)
R5
1
Q = (1 +
)
3
R4
(23)
5. Also
6. Also
1
( ff0 )2
f
j f0
vbp
=
vin
1 − ( ff0 )2 + ( Qj )( ff0 )
(24)
vlp
−1
=
f
2
vin
1 − ( f0 ) + ( Qj )( ff0 )
(25)
Assuming f0 = 1 kHz and the required bandwidth of the band pass filter is 10
Hz, on setting R1 = R6 = R7 = 47kΩ and C1 = C2 = 2.2nF , calculation yields
R2 = R3 = 72.33kΩ10 In this design Q = 1k/10 = 100. Hence setting R4 = 1kΩ
yields R5 = 294kΩ (1 % tolerance). The simulation waveforms for the band pass
10
The values of R2 and R3 need to be trimmed if the filter center frequency and bandwidth
are required to high accuracy.
38
R7
R=47k
number
1
R1
R=47k
R2
R=72.33k
V1.I
8.56 e-11
vbp.V
-0.00149
vhp.V
-0.00149
vlp.V
0.000514
vin
R6
R=47k
R3
R=72.33k
C1
C=2.2n
V1
U=0.1
In-
In-
InOP27
ICMZ
P1P2O
vhp
OP27
ICMZ
P1P2O
In+
R4
R=1k
OP27
ICMZ
P1P2O
vbp
vlp
In+
In+
SUB1
C2
C=2.2n
SUB3
SUB2
R5
R=294 k
dc simulation
DC1
ac simulation
Equation
Eqn1
Av_BP=dB(vbp.v/vin.v)
Av_phase=phase(vbp.v/vin.v)
AC1
Type=lin
Start=100Hz
Stop=1900 Hz
Points=500
Figure 31: Three OP AMP state variable filter.
output are given in Fig. 32 11 . When the circuit Q factor is reduced to lower values
the other filter outputs act as traditional high and low pass filters. The simulation
results for Q factor one are shown in Fig. 33.
Example 2: Sinusoidal signal generation with the Wien
bridge oscillator
The Wien bridge sinusoidal oscillator has become a classic due to it’s simplicity and
low distortion capabilities. It is an ideal vehicle for demonstrating the properties of
OP AMP macromodels and indeed the performance of circuit simulators. Shown
in Fig. 34 is the basic Wien bridge oscillator which consists of a single OP AMP
with negative and positive feedback circuits. The design equations for this circuit
are
1. Non-inverting amplifier.
R3
vout
=1+
v+
R4
(26)
11
Note that the input signal vin has been set at 0.1 V peak. The circuit has a Q factor of 100
which means that the band pass output voltage is 10 V peak. Input signals of amplitude much
greater than 0.1 V are likely to drive the output signal into saturation when the power supply
voltages are ±15V .
39
Av_BP in dB
40
20
0
-20
200
400
600
800
1e3
Frequency Hz
1.2e3
1.4e3
1.6e3
1.8e3
200
400
600
800
1e3
Frequency Hz
1.2e3
1.4e3
1.6e3
1.8e3
AV_phase in degrees
100
50
0
-50
-100
Figure 32: Simulation waveforms for current state variable filter circuit shown in
Fig. 31.
40
vhp.v
0.1
0.05
0
1
10
100
1
10
100
1e3
Frequency Hz
1e4
1e5
1e6
vlp.v
0.1
0.05
0
1e3
Frequency Hz
1e4
1e5
1e6
Figure 33: State variable low pass and high pass response for Q = 1, R5 = 2kΩ.
2. Feedback factor
b=
Where f0 =
vout
1
=
v+
3 + j( ff0 −
f0
)
f
(27)
1
1
=
2πR1C1
2πR2C2
3. Loop gain
The oscillator loop gain bAv must equal one for stable oscillations. Hence,
bAv =
Moreover, at f = f0 ,
1+
R3
R4
3 + j( ff0 −
1 + R3
R4
bAv =
3
f0
)
f
(28)
(29)
Setting R3/R4 slightly greater than two causes oscillations to start and increase in amplitude during each oscillatory cycle. Furthermore, if R3/R4 is
less than two oscillations will never start or decrease to zero.
Figure 35 shows a set of Wien bridge oscillator waveforms. In this example the
OP AMP is modelled using the OP27 AC macromodel. This has been done deliberately to demonstrate what happens with a poor choice of OP AMP model. The
41
oscillator frequency is 10 kHz with both feedback capacitors and resistors having
equal values. Notice that the oscillatory output voltage continues to grow with
increasing time until it’s value far exceeds the limit set by a practical OP AMP
power supply voltages. The lower of the two curves in Fig. 35 illustrates the frequency spectrum of the oscillator output signal. The data for this curve has been
generated using the Time2Freq function. Adding slew rate and voltage limiting to
the OP27 macromodel will limit the oscillator output voltage excursions to the OP
AMP power supply values. The waveforms for this simulation are shown in Fig. 36.
When analysing transient response data using function Time2Freq it is advisable
to restrict the analysis to regions of the response where the output waveform has
reached a steady state otherwise the frequency spectrum will include effects due to
growing, or decreasing, transients. The voltage limiting network clips the oscillator
output voltage restricting its excursions to below the OP AMP power supply voltages. The clipping is very visible in Fig. 36. Notice also that the output waveform
is distorted and is no longer a pure sinusoidal waveform of 10 kHz frequency. Odd
harmonics are clearly visible and the fundamental frequency has also decreased
due to the signal saturation distortion. In a practical Wien bridge oscillator the
output waveform should be a pure sinusoid with zero or little harmonic distortion.
One way to achieve this is to change the amplitude of the OP AMP gain with
changing signal level: as the output signal increases so Av is decreased or as the
output signal level decreases Av is increased. At all times the circuit parameters
are changed to achieve the condition bAv = 1. The circuit shown in Fig. 37 uses
two diodes and a resistor to automatically change the OP AMP closed loop gain
with changing signal level. Fig. 38 shows the corresponding waveforms for the
Wien bridge circuit with automatic gain control. Changing the value of resistor
R5 causes the amplitude of the oscillator output voltage to stabilise at a different
value; decreasing R5 also decreases vout. The automatic gain control version of the
Wien bridge oscillator also reduces the amount of harmonic distortion generated
by the oscillator. This can be clearly observed in Fig. 38. Changing the oscillator
frequency can be accomplished by either changing the capacitor or resistor values
in the feedback network b. To demonstrate how this can be done using Qucs, consider the circuit shown in Fig. 39. In this circuit time controlled switches change
the value of both capacitors as the simulation progresses. The recorded output
waveform for this circuit is shown in Fig. 40.
42
C2
C=1 nF
R2
R=15.8k
R1
R=15.8k
C1
C=1nF
SUB2
File=OP27_ICMZP1P2O.sch
In+
vout
OP27
ICMZ
P1P2O
dc simulation
In-
DC1
transient
simulation
R4
R=10k
TR1
Type=lin
Start=0
Stop=10 ms
R3
R=21k
Equation
Eqn1
y=1
fscan=Time2Freq(vout.Vt,time[700:1000])
Figure 34: Classic Wien bridge sinusoidal oscillator.
vout.Vt
1e11
0
Frequency Spectrum
-1e11
0
1e-3
0.002
0.003
0.004
0.005
time
0.006
0.007
0.008
0.009
0.01
0
5e3
1e4
1.5e4
2e4
2.5e4
Frequency Hz
3e4
3.5e4
4e4
4.5e4
5e4
1e9
0
Figure 35: Simulation waveforms for the circuit shown in Fig. 34: OP27 AC
macromodel.
43
vout.Vt
10
0
-10
0
1e-3
0.002
0.003
0.004
0.005
time
0.006
0.007
0.008
0.009
0.01
Freq-Specrum
6
4
2
0
0
3e3
6e3
9e3
1.2e4
1.5e4
1.8e4
2.1e4
2.4e4 2.7e4
Frequency
3e4
3.3e4
3.6e4
3.9e4
4.2e4
4.5e4
4.8e4
Figure 36: Simulation waveforms for the circuit shown in Fig. 34: OP27 AC +
slew rate + vlimit macromodel.
C2
C=1 nF
R2
R=15.8k
C1
C=1nF
R1
R=15.8k
SUB1
In+
OP27
ICMZ SLWRT
P1P2 VLIM
O
In-
dc simulation
DC1
V1
U=15 V
VEE
vout
V2
U=15 V
VCC
transient
simulation
TR1
Type=lin
Start=0
Stop=10 ms
IntegrationMethod=Trapezoidal
R4
R=10k
R3
R=21k
R5
R=50k
Equation
Eqn1
fscan=Time2Freq(vout.Vt,time[700:1000])
D1
D2
Figure 37: Wien bridge oscillator with automatic gain control.
44
vout.Vt
1
0
-1
0
1e-3
0.002
0.003
0.004
0.005
time
0.006
0.007
0.008
0.009
0.01
Freq-Spectrum
0.4
0.2
0
0
3e3
6e3
9e3
1.2e4
1.5e4
1.8e4
2.1e4
2.4e4 2.7e4
Frequency Hz
3e4
3.3e4
3.6e4
3.9e4
4.2e4
4.5e4
4.8e4
Figure 38: Simulation waveforms for the circuit shown in Fig. 37: OP27 AC +
slew rate + vlimit macromodel.
dc simulation
S6
C8
C=0.0625nF
DC1
C7
C=0.125nF
transient
simulation
C6
C=0.25nF
TR1
Type=lin
Start=0
Stop=10 ms
IntegrationMethod=Trapezoidal
S3
time=8 ms
S1
time=7 ms
C5
C3
C=0.0625nF C=0.125nF
S4
R1
R=15.8k
C1
C=0.5nF
SUB1
S2
time=6 ms
C4
C=0.25nF
S5
C2
C=0.5 nF
In+
OP27
ICMZ SLWRT
R2
R=15.8k P1P2 VLIM
O
In-
R4
R=10k
V1
U=15 V
VEE
vout
V2
U=15 V
VCC
R3
R=21k
R5
R=50k
D1
D2
Figure 39: Wien bridge oscillator with switched capacitor frequency control.
45
vout.Vt
1
0
-1
0
1e-3
0.002
0.003
0.004
0.005
time
0.006
0.007
0.008
0.009
0.01
vout.Vt
1
0
-1
0.005
0.0051
0.0052
0.0053
0.0054
0.0055
0.0056
0.0057
0.0058
0.0059
0.0065
0.0066
0.0067
0.0068
0.0069
0.0075
0.0076
0.0077
0.0078
0.0079
0.0085
0.0086
0.0087
0.0088
0.0089
time
vout.Vt
1
0
-1
0.006
0.0061
0.0062
0.0063
0.0064
time
vout.Vt
1
0
-1
0.007
0.0071
0.0072
0.0073
0.0074
time
vout.Vt
1
0
-1
0.008
0.0081
0.0082
0.0083
0.0084
time
Figure 40: Simulation waveforms for the circuit shown in Fig. 39: OP27 AC +
slew rate + vlimit macromodel.
46
Update number one: March 2007
In this first update to the operational amplifier tutorial readers will be introduced to Qucs macromodel model building using schematics and SPICE to Qucs
conversion techniques, secondly to procedures for constructing Qucs operational
amplifier libraries, and finally to two different approaches which allow existing OP
AMP models to be extended to include new amplifier performance parameters,
for example power supply rejection. This update is very much a report on the
OP AMP modelling work that has been done by the Qucs development team since
version 0.0.10 of the package was released in September 2006. Future Qucs releases
will offer many significant improvements in OP AMP modelling particularly via
SPICE to Qucs netlist conversion, subcircuit passing and equation embedding in
Qucs schematics and library development. Following the release of Qucs 0.0.11,
and a suitable period of time for new feature debugging, many of the ideas introduced in this update will be developed to include OP AMP model building using
embedded equations in Qucs schematics.
Building a library component for the modular OP AMP
macromodel
One of the main strengths of the modular macromodel approach to device modelling is the fact that the parameters implicit in each section of a macromodel are
essentially independent, allowing subcircuit blocks to be easily connected together
to form an overall device model. Taking this idea further one can construct a
complete schematic for an OP AMP model from the circuitry that represents individual macromodel subcircuit blocks. The diagram shown in Fig. 41 illustrates
a typical circuit schematic for a modular OP AMP macromodel. In this schematic
the component values are for the UA741 OP AMP. By attaching a symbol to the
modular macromodel schematic the UA741 modular OP AMP model is ready for
general use and can be placed in an existing12 or a user defined library. Moreover,
by recalculating the component values further library elements can be constructed
and the development of a more extensive Qucs OP AMP library undertaken13 .
12
Qucs 0.0.10, and earlier releases, were distributed with an OP AMP library called OpAmps.
However, this only contained a component level model for the 741 OP AMP. Many of the models
discussed in this text have been added to the Qucs OpAmps library. These should assist readers
who wish to experiment with their own OP AMP circuits.
13
One of the important future tasks is the development of component libraries for use with
Qucs - this will take time but should be possible given enough effort by everyone interested in
Qucs.
47
Voff1
U=0.35m V
Ib1
I=80nA
P_INN
R1
R=1M
RSUM1
R=1
Ioff1
I=10nA
Cin1
C=1.4 pF
Ib2
I=80nA
Voff2
U=0.35m V
SRC1
G=1 S
R2
R=1M
P_INP
RCM1
R=1M
RDCMZ
R=650M
ECM1
G=31.623
RCM2
R=1
SRC2
G=1 S
CCM1
C=795.8 pF
GMSRT1
G=0.01 S
RSCALE1
R=100
SRC3
G=1 S
VSR1
U=7.26 V
CP2
C=53.05nF
GMP2
G=1 S
RDCCL1
R=100M
RADO
R=200k
CP1
C=159.15nF
GMP1
G=1 S
D1
Is=1e-12 A
Bv=14.5
Ibv=20 mA
RP2
R=1
D2
Is=1e-15 A
RSRT1
R=1
ROS1
R=75
P_VCC
EOS1
G=1
VLIM1
U=2 V
DVL1
Is=8e-16 A
D3
Is=1e-15 A
HCL1
G=35
DVLM2
Is=8e-16 A
ECL
G=1
P_OUT
VLIM2
U=2 V
P_VEE
Figure 41: Modular OP AMP macromodel in schematic form - this model does
not include signal overloading.
48
Changing model parameters: use of the SPICEPP preprocessor
Changing the component data in Fig. 41 allows users to generate modular macromodels for different operational amplifiers. Although this is a perfectly viable
approach to model generation it is both tedious and error prone. A more straightforward way is to get the computer to do the tedious work involving component
value calculation from device data. With this approach users are only required
to enter the device data; as a simple list derived from manufacturers data sheets.
One way to do this is to write a SPICE preprocessor template14 and let a SPICE
preprocessor generate the model for a specific OP AMP. The PS2SP template file
for an OP27 OP AMP modular macromodel is given in Fig. 42. The resulting
SPICE file is shown in Fig. 43. After construction of the SPICE OP27 netlist the
Qucs OP27 model is generated via the schematic capture SPICE netlist facility.15
The Boyle operational amplifier SPICE model
The Boyle16 operational amplifier model was one of the earliest attempts at constructing an OP AMP macromodel that achieved significantly reduced simulation
times, when compared to those times obtained with discrete transistor level models17 , while maintaining acceptable functional properties and simulation accuracy.
The Boyle macromodel was designed to model differential gain versus frequency,
DC common-mode gain, device input and output characteristics, slew rate limiting, output voltage swing and short-circuit limiting. The circuit schematic for the
Boyle macromodel of a bipolar OP AMP is illustrated in Fig. 44. This model consists of three connected stages: the input stage, the intermediate voltage gain stage
and the output stage. Calculation of individual component values is complex, relying on a set of equations derived from the physical properties of the semiconductor
devices and the structure of the electrical network. These equations are derived in
the Boyle paper and summerised in the following list. Starting with IS1 =8.0e-16,
the emitter base leakage current of transistor T1, and by assuming R2 = 100k the
14
The use of the SPICE preprocessors SPICEPP and SPICEPRM are described in Qucs tutorial
Qucs simulation of SPICE netlists. Since both SPICEPP and SPICEPRM were first written,
Friedrch Schmidt has developed a PSpice to SPICE3/XSPICE preprocessor which combines,
and extends, the features found in both SPICEPP and SPICEPRM. This preprocessor is called
PS2SP. The Perl script version of PS2SP is licensed under GPL and may be downloaded from
http://members.aon.at/fschmid7/.
15
See the tutorial Qucs simulation of SPICE netlist for instructions on how this can be done.
16
G.R. Boyle, B.M. Cohn, D. Pederson, and J.E. Solomon, Macromodelling of integrated circuit
operational amplifiers, IEEE Journal of Solid State Circuits, vol. SC-9, pp. 353-364, 1974.
17
See Fig. 3. Tests show that the Boyle macromodel reduces simulation times for common
amplifier, timer and filter circuits by a factor between six and ten.
49
model component values can be calculated using:
V OS
V OS ∼
,where V t = 26e-3 V.
1. IS2 = IS1 · exp V t = IS1 1 +
Vt
2. IC1 =
C2 SR+
, where SR+ is the positive slew rate.
2
3. IC2 = IC1
4. IB1 = IB −
IOS
IOS
and IB2 = IB +
2
2
IC2
IC1
and B2 =
IB1
IB2
B1 + 1 B2 + 1
6. IEE =
+
IC1
B1
B2
5. B1 =
7. RC1 =
1
2πGBP C2
8. RC2 = RC1
B1 + B2
1
IC1
9. RE1 =
, and RE2 = RE1
RC1 −
, where gm1 =
2 + B1 + B2
gm1
Vt
C2
π 10. CEE =
· tan 4φ
, where 4φ = 90o − Φm and Φm is the phase
2
180
margin.
11. GCM =
1
CM M RRC1
12. GA =
1
RC1
13. GB =
AvOLRC1
R2RO2
14. ISD1 = IX · exp (T M P 1)+1e-32, where IX = 2 · IC1 · R2 · GB − IS1 ,
−1
and T M P 1 =
IS1
RO1
Vt
15. RC =
Vt
IX
ln (T EM P 2), where T EM P 2 =
100 · IX
ISD1
50
ISCP
16. V C = abs (V CC) − V OU TP + V t · ln
IS1
ISCN
17. V E = abs (V EE) + V OU TN + V T · ln
IS1
18. RP =
(V CC − V EE) (V CC − V EE)
PD
Rather than calculate the Boyle macromodel component values by hand using a
calculator it is better to use a PS2SP preprocessor template that does these calculations and also generates the Boyle SPICE netlist. A template for this task is
given in Fig. 45. The parameters at the beginning of the listing are for the UA741
OP AMP. In Fig. 45 the macromodel internal nodes are indicated by numbers and
external nodes by descriptive names. This makes it easier to attach the macromodel interface nodes to a Qucs schematic symbol. The SPICE netlist shown in
Fig. 46 was generated by SP2SP.
Model accuracy
The modular and Boyle OP AMP macromodels are examples of typical device
models in common use with todays popular circuit simulators. A question which
often crops up is which model is best to use when simulating a particular circuit?
This is a complex question which requires careful consideration. One rule of thumb
worth following is always validate a SPICE/Qucs model before use. Users
can then check that a specific model does simulate the circuit parameters that
control the function and accuracy of the circuit being designed18 . One way to
check the performance of a given model is to simulate a specific device parameter.
The simulation results can then be compared to manufacturers published figures
and the accuracy of a model easily determined. By way of an example consider
the simulation circuit shown in Fig. 47. In this circuit the capacitors and inductors ensure that the devices under test are in ac open loop mode with stable dc
conditions. Figure 48 illustrates the observed simulation gain and phase results for
four different OP AMP models. Except at very high frequencies, which are outside
device normal operating range, good agreement is found between manufacturers
data and that recorded by the open loop voltage gain test for both the modular
and Boyle macromodels.
18
An interesting series of articles by Ron Mancini, on verification and use of SPICE models in
circuit design can be found in the following editions of EDN magazine:Validate SPICE models
before use, EDN March 31, 2005 p.22; Understanding SPICE models, EDN April 14, p 32; Verify
your ac SPICE model, EDN May 26, 2005; Beyond the SPICE model’s dc and ac performance,
EDN June 23 2005, and Compare SPICE-model performance, EDN August 18, 2005.
51
∗ s u b c i r c u i t p o r t s : in+
in−
p out p v c c p v e e
. s u b c k t opamp ac in p in n p out p v c c p v e e
∗ OP27 OP AMP p a r a m e t e r s
. param v o f f = 30 . 0u i b = 15n
i o f f = 12n
. param rd = 4meg cd = 1 . 4p cmrrdc = 1 . 778 e6
. param fcmz = 2000 . 0 a o l d c = 1 . 778 e6 gbp = 8meg
. param f p 2 = 17meg p s l e w r=2 . 8 e6 n s l e w r=2 . 8 e6
. param vccm=15 vpoutm=14 veem=−15
. param vnoutm=−14 idcoutm=32m r o=70 . 0
. param p1={ ( 1 0 0 ∗ p s l e w r ) / ( 2 ∗ 3 . 1412∗ gbp ) −0 . 7}
. param p2={ ( 1 0 0 ∗ n s l e w r ) / ( 2 ∗ 3 . 1412∗ gbp ) −0 . 7}
∗ input stage
v o f f 1 in n 6 { v o f f /2 }
v o f f 2 7 in p { v o f f /2 }
ib1
0 6 {ib}
ib2
7 0 {ib}
i o f f 1 7 6 { i o f f /2 }
r1
6 8 { rd /2 }
r2
7 8 { rd /2 }
c i n 1 6 7 { cd }
∗ common−mode z e r o s t a g e
ecm1 12 0 8 0 {1 e6 / cmrrdc }
rcm1 12 13 1meg
ccm1 12 13 { 1 / ( 2 ∗ 3 . 1412∗1 e6 ∗ fcmz ) }
rcm2 13 0 1
∗ d i f f e r e n t i a l and common−mode s i g n a l summing s t a g e
gmsum1 0 14 7 6 1
gmsum2 0 14 13 0 1
rsum1 14 0 1
∗ slew rate stage
g s r c 1 0 15 13 0 1
r s c a l e 1 15 0 100
d s l 15 16 { d s l e w r a t e }
. model d s l e w r a t e d ( i s=1 e −12 bv= { p1+p2 } )
v s r 1 16 0 {p1}
gmsrt1 0 17 15 0 0 . 01
r s r t 1 17 0 1
∗ voltage gain stage 1
gmp1 0 9 17 0 1
rado 9 0 { a o l d c }
cp1 9 0 { 1 / ( 2 ∗ 3 . 1412∗ gbp ) }
∗ voltage gain stage 2
gmp2 0 11 9 0 1
rp2 11 0 1
cp2 11 0 { 1 / ( 2 ∗ 3 . 1412∗ f p 2 ) }
∗ out put s t a g e
e o s 1 10 0 11 0 1
r o s 1 10 50 { r o }
∗ out put c u r r e n t l i m i t e r s t a g e
r d c l 1 50 0 100meg
d c l 1 21 50 d c l i m
d c l 2 50 21 d c l i m
. model d c l i m d ( i s=1 e −15 c j 0=0 . 0 )
v c l 1 50 p out 0v
h c l 1 0 22 v c l 1 {0 . 9/ idcoutm }
e c l 1 21 22 50 0 1
∗ voltage limiting stage
d v l 1 p out 30 d v l i m i t
. model d v l i m i t d ( i s=8 e −16)
d v l 2 40 p out d v l i m i t
v l i m 1 p v c c 30 { vcc−vccm+1}
v l i m 2 40 p v e e {−v e e +veem+1}
. ends
. end
52
Figure 42: PS2SP template for the OP27 modular macromodel.
∗ s u b c i r c u i t p o r t s : in+ in− p out p v c c p v e e
∗ i n f i l e=op27 . pp d a t e=Tue Feb 13 17 : 32 : 37 2007 Converted with p s 2 s p . p l V4 . 11
∗ o p t i o n s : −sp3=0 − l t s p i c e=0 −fromsub=0 −f r o m l i b=0 −c h e c k=0 ( t i n y l i n e s=1 )
∗ c o p y r i g h t 2007 by F r i e d r i c h Schmidt − terms of Gnu L i c e n c e
. s u b c k t opamp ac in p in n p out p v c c p v e e
v o f f 1 in n 6 1 . 5 e −05
v o f f 2 7 in p 1 . 5 e −05
i b 1 0 6 1 . 5 e −08
i b 2 7 0 1 . 5 e −08
i o f f 1 7 6 6 e −09
r 1 6 8 2000000
r 2 7 8 2000000
c i n 1 6 7 1 . 4 e −12
ecm1 12 0 8 0 0 . 56 2429 6962 8796 4
rcm1 12 13 1meg
ccm1 12 13 7 . 95874188208328 e −11
rcm2 13 0 1
gmsum1 0 14 7 6 1
gmsum2 0 14 13 0 1
rsum1 14 0 1
g s r c 1 0 15 13 0 1
r s c a l e 1 15 0 100
d s l 15 16 0
. model d s l e w r a t e d ( i s=1 e −12 bv= 9 . 7422386349166 )
v s r 1 16 0 4 . 8711193174583
gmsrt1 0 17 15 0 0 . 01
r s r t 1 17 0 1
gmp1 0 9 17 0 1
rado 9 0 1778000
cp1 9 0 1 . 98968547052082 e −08
gmp2 0 11 9 0 1
rp2 11 0 1
cp2 11 0 9 . 36322574362739 e −09
e o s 1 10 0 11 0 1
r o s 1 10 50 70
r d c l 1 50 0 100meg
d c l 1 21 50 d c l i m
d c l 2 50 21 d c l i m
. model d c l i m d ( i s=1 e −15 c j 0=0 . 0 )
v c l 1 50 p out 0v
h c l 1 0 22 v c l 1 28 . 125
e c l 1 21 22 50 0 1
d v l 1 p out 30 d v l i m i t
. model d v l i m i t d ( i s=8 e −16)
d v l 2 40 p out d v l i m i t
v l i m 1 p v c c 30 −14
v l i m 2 40 p v e e −14
. ends
. end
Figure 43: SPICE netlist for the OP27 modular macromodel.
53
P_VCC
VC
RC1
RC2
RP
D3
C1
D1
C2
D2
RO1
GCM
T1
T2
RC
R2
P_INN
RE1
CEE
RE2
IEE
GA
P_OUT
D4
GC
RO2
VE
GB
REE
P_VEE
P_INP
Figure 44: Boyle macromodel for a BJT OP AMP
The PSpice modified Boyle model
One of the most widely used OP AMP simulation models is a modified version
of the Boyle macromodel. This was originally developed for use with the PSpice
circuit simulator. Many semiconductor manufacturers provide models for their devices based on the modified Boyle macromodel19 . A typical modified Boyle macromodel SPICE netlist is shown in Fig. 49. The circuit structure and performance
are very similar, but significantly different to the original Boyle model. Some of
the common OP AMP parameters NOT modeled are (1) input offset voltage, (2)
temperature coefficient of input offset voltage, (3) input offset current, (4) equivalent input voltage and noise currents, (5) common-mode input voltage range, and
(6) temperature effect on component stability. Items (2), (4), (5) and (6) are also
not modeled by the standard Boyle macromodel. Although the modified Boyle
macromodel is similar to the original Boyle model it is not possible to use this
model as it is defined with Qucs; due to the fact that SPICE 2G nonlinear controlled sources, egnd and fb, are included in the SPICE netlist. Controlled source
egnd is employed to model the OP AMP reference voltage as the average of the
VCC and VEE power rail voltages rather than the ground voltage assumed in the
original Boyle macromodel20 . Current conrolled current source fb is used to model
19
See for example the OP AMP section of the Texas Instruments (TI) Web site and the TI
Operational Amplifier Circuits, Linear Circuits, Data Manual, 1990.
20
Taking the OP AMP reference voltage to be the average of VCC and VEE allows devices
with non-symmetrical power supply voltages to be simulated.
54
∗ Boyle macromodel t e m p l a t e f o r Qucs .
∗ D e s i g n p a r a m e t e r s ( For UA741 )
. param v t=26 e−3 $ Thermal v o l t a g e a t room temp .
. param c2=30 e −12
$ Compensation c a p a c i t a n c e
. param p o s i t i v e s l e w r a t e=0 . 625 e6 n e g a t i v e s l e w r a t e=0 . 50 e6 $ Slew r a t e s
. param i s 1=8 . 0 e −16 $ T1 l e a k a g e c u r r e n t
. param v o s=0 . 7 e−3 i b=80n i o s=20n $ I n p u t v o l t a g e and c u r r e n t p a r a m e t e r s
. param va=200 $ Nominal e a r l y v o l t a g e
. param gbp=1 . 0 e6 $ Gain bandwidth p r o d u c t
. param pm=70 $ E x c e s s phase a t u n i t y g a i n .
. param cmrr=31622 . 8 $ Common−mode r e j e c t i o n r a t i o ( 9 0 dB)
. param a v o l=200 k $ DC open l o o p d i f f e r e n t i a l g a i n
. param r o 2=489 . 2 $ DC outpu t r e s i s t a n c e
. param r o 1=76 . 8 $ High f r e q u e n c y AC outp ut r e s i s t a n c e
. param r 2=100 k
. param vout p=14 . 2 $ P o s i t i v e s a t u r a t i o n v o l t a g e − f o r VCC=15 v
. param vout n=−13 . 5 $ N e g a t i v e s a t u r a t i o n v o l t a g e − f o r VCC=−15v
. param v c c=15 $ P o s i t i v e power s u p p l y v o l t a g e
. param v e e=−15 $ N e g a t i v e power s u p p l y v o l t a g e
. param i s c p=25m $ S h o r t c i r c u i t out put c u r r e n t
. param i s c n=25m $ S h o r t c i r c u i t out put c u r r e n t
. param pd=59 . 4m $ T y p i c a l power d i s s i p a t i o n
∗ Design e q u a t i o n s
. param i s 2={ i s 1 ∗(1+ v o s / v t ) }
. param i c 1={0 . 5∗ c2 ∗ p o s i t i v e s l e w r a t e } i c 2={ i c 1 }
. param i b 1={ ib −0 . 5∗ i o s } i b 2={ i b +0 . 5∗ i o s }
. param b1={ i c 1 / i b 1 } b2={ i c 2 / i b 2 }
. param i e e={ ( ( b1 +1)/ b1+(b2 +1)/ b2 ) ∗ i c 1 }
. param gm1={ i c 1 / v t } r c 1={ 1 / ( 2 ∗ 3 . 1412∗ gbp ∗ c2 ) } r c 2=r c 1
. param r e 1={ ( ( b1+b2 )/(2+ b1+b2 ) ) ∗ ( rc1 −1/gm1 ) } r e 2=r e 1
. param r e e={va / i e e } c e e={ ( 2 ∗ i c 1 / n e g a t i v e s l e w r a t e )−c2 }
. param dphi={90−pm} c1={ ( c2 / 2 ) ∗ tan ( dphi ∗3 . 1 4 1 2 / 1 8 0 ) }
. param gcm={ 1 / ( cmrr ∗ r c 1 ) } ga={ 1/ r c 1 } gb={ ( a v o l ∗ r c 1 ) / ( r 2 ∗ r o 2 ) }
. param i x={ 2∗ i c 1 ∗ r 2 ∗gb−i s 1 } tmp1={−1 . 0 / ( r o 1 ∗ i s 1 / v t ) } i s d 1={ i x ∗ exp ( tmp1)+1e −32}
. param tmp2={ i x / i s d 1 } r c={ v t / ( 1 0 0 ∗ i x ) ∗ l n ( tmp2 ) }
. param gc={ 1/ r c }
. param vc={ abs ( v c c )−vout p+vt ∗ l n ( i s c p/ i s 1 ) } ve={ abs ( v e e )+ vout n+vt ∗ l n ( i s c n/ i s 1 ) }
. param rp={ ( vcc−v e e ) ∗ ( vcc−v e e ) / pd}
∗ Nodes : I n p u t n i n p n i n n n v c c n v e e
Output n out
Q1 8 n i n n 10 qmod1
Q2 9 n i n p 11 qmod2
RC1 n v c c 8 { r c 1 }
RC2 n v c c 9 { r c 2 }
RE1 1 10 { r e 1 }
RE2 1 11 { r e 2 }
RE 1 0 { r e e }
CE 1 0 { c e e }
IEE 1 n v e e { i e e }
C1 8 9 { c1 }
RP n v c c n v e e { rp }
GCM 0 12 1 0 {gcm}
GA 12 0 8 9 { ga }
R2 12 0 { r 2 }
C2 12 13 30p
GB 13 0 12 0 {gb}
RO2 13 0 { r o 2 }
RO1 13 n out { r o 1 }
D1 13 14 dmod1
D2 14 13 dmod1
GC 0 14 n out 0 { gc }
RC 14 0 { r c }
D3 n out 15 DMOD3
D4 16 n out DMOD3
VC n v c c 15 { vc }
55
VE 16 n v e e { ve }
. model dmod1 d ( i s={ i s d 1 } r s=1 )
. model dmod3 d ( i s=8 e −16 r s=1 )
. model qmod1 npn ( i s={ i s 1 } BF={b1} )
. model qmod2 npn ( i s={ i s 2 } BF={b2} )
. end
Figure 45: PS2SP template for the Boyle macromodel with UA741 parameters
listed.
∗ b o y l e macromodel t e m p l a t e f o r q u c s .
∗ i n f i l e=ua741 b o y l e . p s 2 s p d a t e=Tue Feb 6 20 : 58 : 12 2007 Converted with p s 2 s p . p l V4 . 11
∗ o p t i o n s : −sp3=0 − l t s p i c e=0 −fromsub=0 −f r o m l i b=0 −c h e c k=0 ( t i n y l i n e s=1 )
∗ c o p y r i g h t 2007 by F r i e d r i c h Schmidt − terms of Gnu L i c e n c e
q1 8 n i n n 10 qmod1
q2 9 n i n p 11 qmod2
r c 1 n v c c 8 5305 . 82792138885
r c 2 n v c c 9 5305 . 82792138885
r e 1 1 10 1820 . 05072213971
r e 2 1 11 1820 . 05072213971
r e 1 0 13192612 . 1372032
c e 1 0 7 . 5 e −12
i e e 1 n v e e 1 . 516 e −05
c1 8 9 5 . 4588124089082 e −12
rp n v c c n v e e 15151 . 5151515152
gcm 0 12 1 0 5 . 96000354174836 e −09
ga 12 0 8 9 0 . 000188472
r 2 12 0 100000
c2 12 13 30p
gb 13 0 12 0 21 . 6918557701915
r o 2 13 0 489 . 2
r o 1 13 n out 76 . 8
d1 13 14 dmod1
d2 14 13 dmod1
gc 0 14 n out 0 1621 . 78603105575
r c 14 0 0 . 0 0 0 6 1 6 6 0 4 1 5 1 7 5 0 5 3 9
d3 n out 15 dmod3
d4 16 n out dmod3
vc n v c c 15 1 . 60789905279489
ve 16 n v e e 2 . 30789905279488
. model dmod1 d ( i s=1 e −32 r s=1 )
. model dmod3 d ( i s=8 e −16 r s=1 )
. model qmod1 npn ( i s=8 e −16 b f=107 . 1 4 2 8 5 7 1 4 2 8 5 7 )
. model qmod2 npn ( i s=8 . 21538461538461 e −16 b f=83 . 3 3 3 3 3 3 3 3 3 3 3 3 3 )
. end
Figure 46: SPICE netlist for the Boyle UA741 macromodel.
56
vout_mod
L1
L=1000H
-
C1
C=1000F
RL
R=2k
R1
R=0.00001
VCC
V2
U=15 V
UA741
(MOD)
+
V1
U=1 V
V3
U=15 V
VEE
SUB1
vout_boyle
C2
C=1000F
L2
L=1000H
Equation
Eqn1
gain_mod_27_dB=dB(vout_mod_27.v)
gain_mod_dB=dB(vout_mod.v)
gain_boyle_dB=dB(vout_boyle.v)
gain_boyle_27_dB=dB(vout_boyle_27.v)
phase_boyle_deg=rad2deg(unwrap(angle(vout_boyle.v)))
phase_boyle_27_deg=rad2deg(unwrap(angle(vout_boyle_27.v)))
phase_mod_deg=rad2deg(unwrap(angle(vout_mod.v)))
phase_mod_27_deg=rad2deg(unwrap(angle(vout_mod_27.v)))
R2
R=0.00001
-
VCC
UA741(Boyle)
VEE
+
SUB2
vout_mod_27
L3
L=1000H
-
C3
C=1000F
RL1
R=2k
R3
R=0.00001
dc simulation
VCC
DC1
OP27
(MOD)
vin
+
ac simulation
VEE
AC1
Type=log
Start=1Hz
Stop=100MHz
Points=200
SUB5
vout_boyle_27
C4
C=1000F
L4
L=1000H
-
RL2
R=2k
R4
R=0.00001
VCC
OP27
(Boyle)
+
VEE
SUB6
Figure 47: Test circuit for simulating OP AMP model open loop voltage gain.
57
0
phase_mod_deg
gain_mod_dB
100
0
-50
-100
-150
1
10
100 1e3 1e4 1e5 1e6 1e7 1e8
acfrequency
phase_boyle_deg
gain_boyle_dB
10
100 1e3 1e4 1e5 1e6 1e7 1e8
acfrequency
1
10
100 1e3 1e4 1e5 1e6 1e7 1e8
acfrequency
0
100
0
-100
-100
-200
1
10
100 1e3 1e4 1e5 1e6 1e7 1e8
acfrequency
0
100
phase_mod_27_deg
gain_mod_27_dB
1
0
-100
-200
10
100 1e3 1e4 1e5 1e6 1e7 1e8
acfrequency
1
100
phase_boyle_27_deg
gain_boyle_27_dB
1
0
10
100 1e3 1e4 1e5 1e6 1e7 1e8
acfrequency
0
-100
-200
1
10
100 1e3 1e4 1e5 1e6 1e7 1e8
acfrequency
1
10
100 1e3 1e4 1e5 1e6 1e7 1e8
acfrequency
Figure 48: Open loop voltage gain simulation waveforms for the modular and
Boyle UA741 and OP27 macromodels.
58
OP AMP output current limiting. The nonlinear polynomial21 form of controlled
sources were included in the 2G series of SPICE simulators to allow behavioural
models of summers, multipliers, buffers and other important functional components to be easily constructed. Single and multidimensional polynomial forms of
controlled sources are defined by SPICE 2G. Taking (1) the voltage controlled voltage source and (2) the current controlled current sources as examples the syntax
is as follows:
Ename N(+) N(-) POLY(n) NC1(+) NC1(-) NC2(+) NC2(-)..... P0 P1 P2......,
where n indicates the order of the polynomial with coefficients P0 .....Pn, and
NCn(+), NCn(-) etc are the control node pairs.
This becomes:
• For POLY(1) 22 : Ename N(+) N(-) P0 P1 P2.........
• For POLY(2): Ename N(+) N(-) POLY(2) NC1(+) NC1(-) NC2(+) NC(-) P0 P1 P2......
• For POLY(3): Ename N(+) N(-) POLY(3) NC1(+) NC1(-) NC2(+) NC2(-) NC3(+) NC3() P0 P1 P2....
and so on.
Similarly: Fname N(+) N(-) POLY(n) V1 V2 V3 ...... P0 P1 P2 ....., where V1, V2 .... are
independent voltage sources whose current controls the output. This becomes:
• For POLY(1): Fname N(+) N(-) V1 P0 P1 P2........
• For POLY(2): Fname N(+) N(-) POLY(2) V1 V2 P0 P1 P2.......
• For POLY(3): Fname N(+) N(-) POLY(3) V1 V2 V3 P0 P1 P2 P3......., and so on.
The meaning of the coefficients in the nonlinear controlled source definitions depends on the dimension of the polynomial. The following examples indicate how
SPICE calculates current or voltage values.
• For POLY(1):
The polynomial function f v is calculated using
f v = P 0 + (P 1 ∗ f a) + (P 2 ∗ f a2 ) + (P 3 ∗ f a3 ) + (P 4 ∗ f a4 ) + .........,
where f a is either a voltage or current independent variable.
21
The definition of these polynomial functions was changed in the SPICE 3 series simulators
to a more conventional algebraic form when specifying the B type source components. This
often gives compatibility problems when attempting to simulate SPICE 2 models with circuit
simulators developed from SPICE 3f4 or earlier simulators. Most popular SPICE based circuit
simulators now accept both types of nonlinear syntax.
22
If only one P coefficient is given in the single dimension polynomial case, then SPICE
assumes that this is P1 and that P0 equals zero. Similarly if the POLY keyword is not explicitly
stated in a controlled source definition then it is assumed by SPICE to be POLY(1).
59
• For POLY(2):
The polynomial function f v is calculated using
f v = P 0 + (P 1 ∗ f a) + (P 2 ∗ f b) + (P 3 ∗ f a2 ) + (P 4 ∗ f a ∗ f b) + (P 5 ∗
f b2 ) + (P 6 ∗ f a3 ) +(P 7 ∗ f a2 ∗ f b) + .........., where f a and f b are both either
voltage or current independent variables.
• For POLY(3):
The polynomial function f v is calculated using
f v = P 0 + (P 1 ∗ f a) + (P 2 ∗ f b) + (P 3 ∗ f c) + (P 4 ∗ f a2 ) + (P 5 ∗ f a ∗ f b)
+(P 6 ∗ f a ∗ f c) + (P 7 ∗ f b2 ) + (P 8 ∗ f b ∗ f c) + (P 9 ∗ f c2 ) + (P 10 ∗ f a3 )
+(P 11 ∗ f a2 ∗ f b) + (P 12 ∗ f a2 ∗ f c) + (P 13 ∗ f a ∗ f b2 ) + (P 14 ∗ f a ∗ f b ∗ f c)
+(P 15 ∗ f a ∗ f c2 ) + (P 16 ∗ f b3 ) + (P 17 ∗ f b2 ∗ f c) + (P 18 ∗ f b ∗ f c2 )
+(P 19 ∗ f c3 )............., where f a, f b, and f c are all either voltage or current independent variables.
From Fig. 49 the controlled generators egnd and fb are:
• egnd 99 0 poly(2) (3,0) (4,0) 0 .5 .5
Which is the same as egnd 99 0 poly(2) 3 0 4 0 0 0.5 0.5
By comparison with the SPICE polynomial equations for controlled sources,
V (3) V (4)
+
implying that the controlled voltage source V (egnd)
V (egnd) =
2
2
is the sum of two linear voltage sources.
• fb 7 99 poly(5) vb vc ve vlp vln 0 10.61E6 -10E6 10E6 10E6 -10E6
By comparison with the SPICE polynomial equations for controlled sources
I(fb) = 10.61e6*I(vb) - 10e6*I(vc) + 10e6*I(ve) + 10e6*I(vlp) -10e6*I(vlp)
implying that the controlled current I(f b) is the sum of five linear controlled
current sources.
SPICE sources engd and fb can therefore be replaced in the modified Boyle model
by the following SPICE code23 :
* egnd 99 0 poly(2) (3,0) (4,0) 0 .5 .5
* Forms voltage source with output
* V=0.5*V(4)+0.5*V(3)
egnd1 999 0 4 0 0.5
23
It is worth noting that the code for the polynomial form of controlled sources can only be
replaced by a series connection of linear controlled voltage sources or a parallel connection of
linear controlled current sources provided no higher order polynomial coefficients are present in
the original SPICE code. Some SPICE models use these higher order coefficients to generate
multiply functions. Such cases cannot be converted to code which will simulate using Qucs
0.0.10. Sometime in the future this restriction will be removed when nonlinear voltage and
current sources are added to Qucs.
60
egnd2 99 999 3 0 0.5
*
*fb 7 99 poly(5) vb vc ve vlp vln 0 10.61e6 -10e6 10e6 10e6 -10e6
*
* Forms current source with output
* I=10.61e6*i(vb)-10e6*i(vc)+10e6*i(ve)+10e6*i(vlp)-10e6*i(vln)
*
*Sum 5 current sources to give fb.
fb1 7 99 vb 10.61e6
fb2 7 99 vc -10e6
fb3 7 99 ve 10e6
fb4 7 99 vlp 10e6
fb5 7 99 vln -10e6
Modified Boyle macromodels are often generated using the PSpice Parts24 program.
Such models have similar structured SPICE netlists with different component values. However, changes in technology do result in changes in the input stage that
reflect the use of npn, pnp and JFET input transistors in real OP AMPs. Hence
to use manufacturers published modified Boyle models with Qucs all that is required is the replacement of the SPICE polynomial controlled sources with linear
sources and the correct component values. Again this is best done using a SPICE
preprocessor template. The templates for OP AMPS with npn and PJF input
transistors are shown in Figures 50 and 51. The SPICE netlists shown in Figs. 52
and 53 were generated by the PS2SP preprocessor. For OP AMPS with pnp input
transistors simply change the BJT model reference from npn to pnp and use the
same template.
24
The Parts modelling program is an integral component in the PSpice circuit simulation software originally developed by the MicroSim Corporation, 1993, The Design Centre:Parts (Irvine,
Calif.). It now forms part of Cadence Design Systems OrCad suite of CAD software.
61
∗ connections :
non−i n v e r t i n g i n p u t
∗
|
i n v e r t i n g input
∗
|
|
p o s i t i v e power s u p p l y
∗
|
|
|
n e g a t i v e power s u p p l y
∗
|
|
|
|
out put
∗
|
|
|
|
|
. s u b c k t uA741
1 2 3 4 5
∗
c1
11 12 8 . 661E−12
c2
6 7 30 . 00E−12
dc
5 53 dx
de
54 5 dx
d l p 90 91 dx
d l n 92 90 dx
dp
4 3 dx
egnd 99 0 p o l y ( 2 ) ( 3 , 0 ) ( 4 , 0 ) 0 . 5 . 5
fb
7 99 p o l y ( 5 ) vb vc ve v l p v l n 0 10 . 61E6 −10E6 10E6 10E6 −10E6
ga
6 0 11 12 188 . 5E−6
gcm
0 6 10 99 5 . 961E−9
iee
10 4 dc 15 . 16E−6
hlim 90 0 v l i m 1K
q1
11 2 13 qx
q2
12 1 14 qx
r2
6 9 100 . 0E3
rc1
3 11 5 . 305E3
rc2
3 12 5 . 305E3
r e 1 13 10 1 . 836E3
r e 2 14 10 1 . 836E3
r e e 10 99 13 . 19E6
ro1
8 5 50
ro2
7 99 100
rp
3 4 18 . 16E3
vb
9 0 dc 0
vc
3 53 dc 1
ve
54 4 dc 1
v l i m 7 8 dc 0
v l p 91 0 dc 40
vln
0 92 dc 40
. model dx D( I s=800 . 0E−18 Rs=1 )
. model qx NPN( I s=800 . 0E−18 Bf=93 . 7 5 )
. ends
Figure 49: PSpice modified Boyle macromodel for the UA741 OP AMP.
62
∗ M o d i f i e d Boyle OP AMP model t e m p l a t e
∗ npn BJT i n p u t d e v i c e s .
∗
∗UA741C OP AMP p a r a m e t e r s , m a n u f a c t u r e r Texas I n s t r u m e n t s
. param c1=4 . 664 p c2=20 . 0p
. param ep1=0 . 5 ep2=0 . 5
. param f p 1=10 . 61 e6 f p 2=−10e6 f p 3=10 e6 f p 4=10 e6 f p 5=−10e6
. param vc=2 . 6 ve=2 . 6 v l p=25 v l n=25
. param ga=137 . 7 e−6 gcm=2 . 57 e−9
. param i e e=10 . 16 e−6 hlim=1k
. param r 2=100 k
. param r c 1=7 . 957 k r c 2=7 . 957 k
. param r e 1=2 . 74 k r e 2=2 . 74 k
. param r e e=19 . 69 e6 r o 1=150 r o 2=150
. param rp=18 . 11 k
∗
. s u b c k t ua741 TI P INP P INN P VCC P VEE P OUT
c1 11 12 { c1 }
c2 6 7 { c2 }
dc P OUT 53 dx
de 54 P OUT dx
d l p 90 91 dx
d l n 92 90 dx
∗ egnd 99 0 p o l y ( 2 ) ( 3 , 0 ) ( 4 , 0 ) 0 0 . 5 0 . 5
∗ Qucs m o d i f i c a t i o n , Mike Brinson , Feb 2007
egnd1 999 0 P VCC 0 { ep1 }
egnd2 99 999 P VEE 0 { ep2 }
∗ f b 7 99 p o l y ( 5 ) vb vc ve v l p v l n 0 10 . 61 e6 −10e6 10 e6 10 e6 −10e6
∗ Forms c u r r e n t s o u r c e with out put
∗ I=10 . 61 e6 ∗ i ( vb)−10 e6 ∗ i ( vc )+10 e6 ∗ i ( ve )+10 e6 ∗ i ( v l p )−10 e6 ∗ i ( v l n )
∗ Qucs m o d i f i c a t i o n , Mike Brinson , Feb 2007 .
∗Sum 5 c u r r e n t s o u r c e s t o g i v e f b .
f b 1 7 99 vb { f p 1 }
f b 2 7 99 vc { f p 2 }
f b 3 7 99 ve { f p 3 }
f b 4 7 99 v l p { f p 4 }
f b 5 7 99 v l n { f p 5 }
∗
ga 6 0 11 12 { ga }
gcm 0 6 10 99 {gcm}
i e e 10 P VEE { i e e }
hlim 90 0 v l i m { hlim }
q1 11 P INN 13 qx
q2 12 P INP 14 qx
r 2 6 9 100 k
r c 1 P VCC 11 { r c 1 }
r c 2 P VCC 12 { r c 2 }
r e 1 13 10 { r e 1 }
r e 2 14 10 { r e 2 }
r e e 10 99 { r e e }
r o 1 8 P OUT { r o 1 }
r o 2 7 99 { r o 2 }
rp P VCC P VEE { rp }
vb 9 0 dc 0
vc P VCC 53 dc { vc }
ve 54 P VEE dc { ve }
v l i m 7 8 dc 0
v l p 91 0 dc { v l p }
v l n 0 92 dc { v l p }
. model dx d ( i s=800 . 0 e −18)
. model qx npn ( i s=800 . 0 e −18 b f=62 . 5 )
. ends
. end
63
Figure 50: Modified Boyle PS2SP netlist for the UA741 OP AMP.
∗ M o d i f i e d Boyle OP AMP model t e m p l a t e
∗ JFET i n p u t d e v i c e s .
∗
∗TL081 OP AMP p a r a m e t e r s , m a n u f a c t u r e r Texas I n s t r u m e n t s
. param c1=3 . 498 p c2=15 . 0p
. param ep1=0 . 5 ep2=0 . 5
. param f p 1=4 . 715 e6 f p 2=−5e6 f p 3=5 e6 f p 4=5 e6 f p 5=−5e6
. param vc=2 . 2 ve=2 . 2 v l p=25 v l n=25
. param ga=282 . 8 e−6 gcm=8 . 942 e−9
. param i s s=195 . 0 e−6 hlim=1k
. param r 2=100 k
. param rd1=3 . 536 k rd2=3 . 536 k
. param r s s=1 . 026 e6 r o 1=150 r o 2=150
. param rp=2 . 14 k
∗
. s u b c k t ua741 TI P INP P INN P VCC P VEE P OUT
c1 11 12 { c1 }
c2 6 7 { c2 }
dc P OUT 53 dx
de 54 P OUT dx
d l p 90 91 dx
d l n 92 90 dx
∗ egnd 99 0 p o l y ( 2 ) ( 3 , 0 ) ( 4 , 0 ) 0 0 . 5 0 . 5
∗ Qucs m o d i f i c a t i o n , Mike Brinson , Feb 2007
egnd1 999 0 P VCC 0 { ep1 }
egnd2 99 999 P VEE 0 { ep2 }
∗ f b 7 99 p o l y ( 5 ) vb vc ve v l p v l n 0 10 . 61 e6 −10e6 10 e6 10 e6 −10e6
∗ Forms c u r r e n t s o u r c e with out put
∗ I=10 . 61 e6 ∗ i ( vb)−10 e6 ∗ i ( vc )+10 e6 ∗ i ( ve )+10 e6 ∗ i ( v l p )−10 e6 ∗ i ( v l n )
∗ Qucs m o d i f i c a t i o n , Mike Brinson , Feb 2007 .
∗Sum 5 c u r r e n t s o u r c e s t o g i v e f b .
f b 1 7 99 vb { f p 1 }
f b 2 7 99 vc { f p 2 }
f b 3 7 99 ve { f p 3 }
f b 4 7 99 v l p { f p 4 }
f b 5 7 99 v l n { f p 5 }
∗
ga 6 0 11 12 { ga }
gcm 0 6 10 99 {gcm}
i s s P VCC 10 { i s s }
hlim 90 0 v l i m { hlim }
j 1 11 P INN 10 j x
j 2 12 P INP 10 j x
r 2 6 9 100 k
rd1 P VEE 11 { rd1 }
rd2 P VEE 12 { rd2 }
r o 1 8 P OUT { r o 1 }
r o 2 7 99 { r o 2 }
rp P VCC P VEE { rp }
r s s 10 99 { r s s }
vb 9 0 dc 0
vc P VCC 53 dc { vc }
ve 54 P VEE dc { ve }
v l i m 7 8 dc 0
v l p 91 0 dc { v l p }
v l n 0 92 dc { v l p }
. model dx d ( i s=800 . 0 e −18)
. model j x p j f ( i s=15 . 0 e −12 b e t a=270 . 1 e−6 v t o=−1)
. ends
. end
Figure 51: Modified Boyle PS2SP netlist for the TL081 OP AMP.
64
∗ m o d i f i e d b o y l e op amp model t e m p l a t e
∗ i n f i l e=Mod b o y l e t e m p l a t e npn . pp d a t e=Thu Feb 8 23 : 54 : 59 2007 Converted with p s 2 s p . p l V4 . 11
∗ o p t i o n s : −sp3=1 − l t s p i c e=0 −fromsub=0 −f r o m l i b=0 −c h e c k=0 ( t i n y l i n e s=1 )
∗ c o p y r i g h t 2007 by F r i e d r i c h Schmidt − terms of Gnu L i c e n c e
. s u b c k t ua741 t i p i n p p i n n p v c c p v e e p out
c1 11 12 4 . 664 e −12
c2 6 7 2 e −11
dc p out 53 dx
de 54 p out dx
d l p 90 91 dx
d l n 92 90 dx
egnd1 999 0 p v c c 0 0 . 5
egnd2 99 999 p v e e 0 0 . 5
f b 1 7 99 vb 9 . 42507068803016 e −08
f b 2 7 99 vc −1e −07
f b 3 7 99 ve 1 e −07
f b 4 7 99 v l p 1 e −07
f b 5 7 99 v l n −1e −07
ga 6 0 11 12 0 . 0001377
gcm 0 6 10 99 2 . 57 e −09
i e e 10 p v e e 1 . 016 e −05
hlim 90 0 v l i m 0 . 001
q1 11 p i n n 13 qx
q2 12 p i n p 14 qx
r 2 6 9 100 k
r c 1 p v c c 11 7957
r c 2 p v c c 12 7957
r e 1 13 10 2740
r e 2 14 10 2740
r e e 10 99 19690000
r o 1 8 p out 150
r o 2 7 99 150
rp p v c c p v e e 18110
vb 9 0 0
vc p v c c 53 2 . 6
ve 54 p v e e 2 . 6
vlim 7 8 0
v l p 91 0 25
v l n 0 92 25
. model dx d ( i s=800 . 0 e −18)
. model qx npn ( i s=800 . 0 e −18 b f=62 . 5 )
. ends
. end
Figure 52: Modified Boyle SPICE netlist for the TI UA741 OP AMP.
65
∗ m o d i f i e d b o y l e op amp model t e m p l a t e
∗ i n f i l e=TL081 TI . pp d a t e=Sun Feb 11 16 : 04 : 22 2007 Converted with p s 2 s p . p l V4 . 11
∗ o p t i o n s : −sp3=0 − l t s p i c e=0 −fromsub=0 −f r o m l i b=0 −c h e c k=0 ( t i n y l i n e s=1 )
∗ c o p y r i g h t 2007 by F r i e d r i c h Schmidt − terms of Gnu L i c e n c e
. s u b c k t ua741 t i p i n p p i n n p v c c p v e e p out t i m e s
c1 11 12 3 . 498 e −12
c2 6 7 1 . 5 e −11
dc p out 53 dx
de 54 p out dx
d l p 90 91 dx
d l n 92 90 dx
egnd1 999 0 p v c c 0 0 . 5
egnd2 99 999 p v e e 0 0 . 5
f b 1 7 99 vb 4715000
f b 2 7 99 vc −5000000
f b 3 7 99 ve 5000000
f b 4 7 99 v l p 5000000
f b 5 7 99 v l n −5000000
ga 6 0 11 12 0 . 0002828
gcm 0 6 10 99 8 . 942 e −09
i s s p v c c 10 0 . 000195
hlim 90 0 v l i m 1000
j 1 11 p i n n 10 j x
j 2 12 p i n p 10 j x
r 2 6 9 100 k
rd1 p v e e 11 3536
rd2 p v e e 12 3536
r o 1 8 p out 150
r o 2 7 99 150
rp p v c c p v e e 2140
r s s 10 99 1026000
vb 9 0 dc 0
vc p v c c 53 dc 2 . 2
ve 54 p v e e dc 2 . 2
v l i m 7 8 dc 0
v l p 91 0 dc 25
v l n 0 92 dc 25
. model dx d ( i s=800 . 0 e −18)
. model j x p j f ( i s=15 . 0 e −12 b e t a=270 . 1 e−6 v t o=−1)
. ends
. end
Figure 53: Modified Boyle SPICE netlist for the TI TL081 OP AMP.
66
Constructing Qucs OPAMP libraries
Qucs release 0.0.10 includes a facility which allows users to build their own component libraries. This facility can be used to construct any library which contains
device models formed using the standard schematic entry route provided the individual components that make up a model do not contain components that require
file netlists. Qucs, for example, converts SPICE netlists to Qucs formated netlists
when a simulation is performed but does not retain the converted netlists. Hence,
to add OP AMP macromodels that are based on SPICE netlist to a Qucs library
a slightly modified procedure is required that involves users copying the converted
SPICE netlist into a Qucs library. One way for generating SPICE netlist based
OP AMP models is as follows25 :
1. Construct a Qucs OP AMP model using the procedure described on page 3
of the Qucs Simulation of SPICE Netlists tutorial.
2. Add this model to a user defined library using the Qucs Create Library
facility (short cut Ctrl+Shift+L).
3. Place a copy of the OP AMP model on a drawing sheet and undertake a
DC analysis. NOTE: drag and drop the model symbol of the device you are
simulating from your current work project and NOT from the newly created
Qucs library.
4. Copy the section of the Qucs netlist that has been converted from the model’s
SPICE netlist and paste this into the newly created library model. The
converted SPICE netlist can be displayed by pressing key F6. User generated
library files are held in directory user_lib.26
To demonstrate the procedure consider the following example based on the UA741
Boyle model:
Steps 1 and 2 result in the following entry in a user created library:
<Component ua741 ( b o y l e )>
<D e s c r i p t i o n >
UA741 Boyle macromodel
</ D e s c r i p t i o n >
<Model>
net0 net1 net2 net3 net4
. Def : Lib OPAMP ua741 b o y l e
Sub : X1 n e t 0 n e t 1 n e t 2 n e t 3 n e t 4 gnd Type=”ua741 b o y l e c i r ”
. Def : End
25
The procedure presented here must be considered a work around and may change as Qucs
develops.
26
The location of the user created libraries will differ from system to system depending where
.qucs is installed.
67
</Model>
<Symbol>
<. ID −20 74 SUB>
<L i n e −20 60 0 −125 #00007 f 2 1>
<L i n e −20 −65 100 65 #00007 f 2 1>
<L i n e −20 60 100 −60 #00007 f 2 1>
<L i n e −35 −35 15 0 #00007 f 2 1>
<L i n e −35 40 15 0 #00007 f 2 1>
<L i n e 80 0 15 0 #00007 f 2 1>
<. PortSym −35 −35 1 0>
<. PortSym −35 40 2 0>
<. PortSym 95 0 3 180>
<L i n e 60 50 0 −40 #00007 f 2 1>
<L i n e 60 −15 0 −40 #00007 f 2 1>
<Text −15 −55 30 #000000 0 ”−”>
<Text −15 30 20 #000000 0 ”+”>
<Text −15 −5 12 #000000 0 ”UA741 ( Boyle ) ”>
<. PortSym 60 −55 4 180>
<. PortSym 60 50 5 180>
<Text 65 −30 12 #000000 0 ”VCC”>
<Text 65 20 12 #000000 0 ”VEE”>
</Symbol>
</Component>
Note that the model requires a subcircuit of type ua741_boyle_cir which is not
included when the library is created by Qucs. After completing the cut and paste
operation described in steps 3 and 4 above the resulting library entry becomes the
Qucs netlist shown next.
<Component ua741 ( b o y l e )>
<D e s c r i p t i o n >
UA741 Boyle macromodel
</ D e s c r i p t i o n >
<Model>
net0 net1 net2 net3 net4
. Def : Lib OPAMP ua741 b o y l e
Sub : X1 n e t 0 n e t 1 n e t 2 n e t 3 n e t 4 gnd Type=”ua741 b o y l e c i r ”
. Def : End
. Def : ua741 b o y l e c i r
netN INN netN INP netN OUT netN VCC netN VEE r e f
Vdc :VE n e t 1 6 netN VEE U=”2 . 3079 ”
Vdc :VC netN VCC n e t 1 5 U=”1 . 6079 ”
Diode : D4 netN OUT n e t 1 6 I s=”8 e −16 ” Rs=”1 ” N=”1 ” M=”0 . 5 ” Cj0=”1 e −14 ” Vj=”0 . 7 ”
Diode : D3 n e t 1 5 netN OUT I s=”8 e −16 ” Rs=”1 ” N=”1 ” M=”0 . 5 ” Cj0=”1 e −14 ” Vj=”0 . 7 ”
R:RC n e t 1 4
r e f R=”0 . 000616604 ”
VCCS:GC netN OUT r e f
net14
r e f G=”1621 . 79 ”
Diode : D2 n e t 1 3 n e t 1 4 I s=”1 e −32 ” Rs=”1 ” N=”1 ” M=”0 . 5 ” Cj0=”1 e −14 ” Vj=”0 . 7 ”
Diode : D1 n e t 1 4 n e t 1 3 I s=”1 e −32 ” Rs=”1 ” N=”1 ” M=”0 . 5 ” Cj0=”1 e −14 ” Vj=”0 . 7 ”
R:RO1 n e t 1 3 netN OUT R=”76 . 8 ”
R:RO2 n e t 1 3
r e f R=”489 . 2 ”
VCCS:GB n e t 1 2 n e t 1 3
ref
r e f G=”21 . 6919 ”
C: C2 n e t 1 2 n e t 1 3 C=”30p ”
R: R2 n e t 1 2
r e f R=”100000 ”
VCCS:GA n e t 8 n e t 1 2
ref
n e t 9 G=”0 . 000188472 ”
VCCS:GCM n e t 1
ref
net12
r e f G=”5 . 96 e −09 ”
R:RP netN VCC netN VEE R=”15151 . 5 ”
C: C1 n e t 8 n e t 9 C=”5 . 45881 e −12 ”
I d c : IEE netN VEE n e t 1 I=”1 . 516 e −05 ”
C:CE n e t 1
r e f C=”0 ”
R:RE n e t 1
r e f R=”1 . 31926 e+07 ”
R: RE2 n e t 1 n e t 1 1 R=”1820 . 05 ”
R: RE1 n e t 1 n e t 1 0 R=”1820 . 05 ”
R: RC2 netN VCC n e t 9 R=”5305 . 83 ”
68
R: RC1 netN VCC n e t 8 R=”5305 . 83 ”
BJT : Q2 netN INP n e t 9 n e t 1 1
r e f Type=”npn ” I s=”8 . 21538 e −16 ” Bf=”83 . 3333 ” Nf=”1 ” Nr=”1 ” I k f=”0 ”
I k r=”0 ” Vaf=”0 ” Var=”0 ” I s e=”0 ” Ne=”1 . 5 ” I s c=”0 ” Nc=”2 ” Br=”1 ” Rbm=”0 ” I r b=”0 ” Cje=”0 ” Vje=”0 . 75 ”
Mje=”0 . 33 ” Cjc=”0 ” Vjc=”0 . 75 ” Mjc=”0 . 33 ” Xcjc=”1 ” C js=”0 ” Vjs=”0 . 75 ” Mjs=”0 ” Fc=”0 . 5 ” Vtf=”0 ”
Tf=”0 ” Xtf=”0 ” I t f=”0 ” Tr=”0 ”
r e f Type=”npn ” I s=”8 e −16 ” Bf=”107 . 143 ” Nf=”1 ”
BJT : Q1 netN INN n e t 8 n e t 1 0
Nr=”1 ” I k f=”0 ” I k r=”0 ” Vaf=”0 ” Var=”0 ” I s e=”0 ” Ne=”1 . 5 ” I s c=”0 ” Nc=”2 ” Br=”1 ”
Rbm=”0 ” I r b=”0 ” Cje=”0 ” Vje=”0 . 75 ” Mje=”0 . 33 ” Cjc=”0 ” Vjc=”0 . 75 ” Mjc=”0 . 33 ”
Xcjc=”1 ” C js=”0 ” Vjs=”0 . 75 ” Mjs=”0 ” Fc=”0 . 5 ” Vtf=”0 ” Tf=”0 ” Xtf=”0 ” I t f=”0 ” Tr=”0 ”
. Def : End
</Model>
<Symbol>
<. ID −20 74 SUB>
<L i n e −20 60 0 −125 #00007 f 2 1>
<L i n e −20 −65 100 65 #00007 f 2 1>
<L i n e −20 60 100 −60 #00007 f 2 1>
<L i n e −35 −35 15 0 #00007 f 2 1>
<L i n e −35 40 15 0 #00007 f 2 1>
<L i n e 80 0 15 0 #00007 f 2 1>
<. PortSym −35 −35 1 0>
<. PortSym −35 40 2 0>
<. PortSym 95 0 3 180>
<L i n e 60 50 0 −40 #00007 f 2 1>
<L i n e 60 −15 0 −40 #00007 f 2 1>
<Text −15 −55 30 #000000 0 ”−”>
<Text −15 30 20 #000000 0 ”+”>
<Text −15 −5 12 #000000 0 ”UA741 ( Boyle ) ”>
<. PortSym 60 −55 4 180>
<. PortSym 60 50 5 180>
<Text 65 −30 12 #000000 0 ”VCC”>
<Text 65 20 12 #000000 0 ”VEE”>
</Symbol>
</Component>
Extending existing OP AMP models
The modular, Boyle and modified Boyle OP AMP models are three popular macromodels selected from a large number of different models that are in common use
today. Most device manufacturers provide similar macromodels, or extended versions which more accurately model the performance of specific devices. Indeed, a
growing trend has developed which mixes Boyle type models with modular structures27 . Often, in practical design projects specific OP AMP properties must be
simulated which are not modelled with an available OP AMP model. Two approaches can be used to overcome such deficiencies; firstly, a macromodel itself
can be modified so that it models the required additional attributes, or secondly
external components can be added which again extend model performance.
One important OP AMP parameter that the standard and modified Boyle models
do not model is the frequency dependence of amplifier common-mode gain. Only
27
See for example: Ray Kendall, User-friendly model simplifies SPICE OP-AMP simulation,
EDN magazine, January 4, 2007, pp. 63-69.
69
the dc value of the CMRR is modelled. Such frequency dependency can be added
by a simple modification28 , requiring one extra node, that simulates ac CMRR
and gives close agreement between macromodel performance and data sheet specifications. Components CEE, REE and GCM, see Fig. 44, are replaced by the
network shown in Fig. 54. Data sheets for the UA741 show the CMRR falling
above a break frequency of about 200 Hz, due to the zero generated by CEE causing the common-mode gain to increase. This effect can be simulated in the Boyle
macromodel by the addition of one extra node and two extra resistors and changes
to REE and controlled source GCM as in Fig. 44. In this modified network, the
common-mode voltage is detected at the junction of RE4 and CEE, introducing
a zero into the response and attenuating the signal. The frequency of the zero
1
. The new value of CEE must have the same value as the
is set by 2∗π∗CEE∗RE3
29
original CEE value if the same slew-rate is to be maintained, so for a 200 Hz
cut-off this gives RE3=106.1M. RE4 is arbitrarily fixed at 10 Ω, which introduces
another pole at about 2 GHz, well outside the frequency of interest. The value
of REE is increased to RE5 (15.06meg), so that RE5 in parallel with RE3 equals
maintaining
the original value of REE. GCM is also increased by the factor RE3
RE4
the correct low frequency common-mode gain. Differential frequency response and
slew rate are unchanged by these modifications. The simulation results for the
common-mode test circuit shown in Fig. 20 are given in Fig. 55. These indicate
close agreement between the modular and ac Boyle macromodels.
Modifying the circuit of an existing OP AMP macromodel is at best a complex
process or at worst impossible because the model details are either not known
or well understood. One way to add features to an existing model is to add an
external circuit to a model’s terminals. This circuit acts as a signal processing
element adding additional capabilities to the original macromodel. One circuit
feature not modelled by any of the macromodels introduced in earlier sections
is power supply rejection. By adding a simple passive electrical network to the
terminals of a macromodel it is possible to model OP AMP power supply rejection.
Power supply rejection(PSRR) is a measure of the ability of an OP AMP to reject
unwanted signals that enter at the power terminals. It is defined as the ratio of
differential-mode gain to power supply injected signal gain. The simulation of OP
28
This section is based on unpublished work by David Faulkner and Mike Brinson., Department
of Computing, Communications Technology and Mathematical Sciences, London Metropolitan
University, UK.
29
In the Boyle macromodel the value of CEE is set by the OP AMP slew rate. Adjusting both
the positive and negative slew rates changes the value of CEE. For the UA741 these have been
set at 0.625e6 and 0.500e6 respectively. This gives CEE=7.5pF which is commonly quoted for
the UA741 value of CEE, see Andrei Vladimirescu, The SPICE Book,1994, John Wiley and Sons,
Inc., ISBN 0-471-60926-9, pp 228-239. Also note care must be taken when choosing values for
the two slew rates because negative values of CEE can occur which are physically not realisable.
70
CEE
C=7.5p
RE3
R=106.1M
RE5
R=15.06M
GCM
G=6.32e-2
RE4
R=10
Figure 54: AC CMRR modification for Boyle macromodel
AMP power supply rejection30 is possible using the test circuit given in Fig. 56,
where
+
V +V−
±
+
−
+ AP S (f )± VS ,
Vout (f ) = AD (f ) [V − V ] + ACM (f )
2
where AD (f ) is the OP AMP differential-mode gain, ACM (f ) is the OP AMP
common-mode gain, and AP S (f )± is the OP AMP power supply injected gain.
The superscript ± indicates that the ac signal source is connected to either the OP
AMP positive or negative power supply terminals but not simultaneously to both.
Assuming that the OP AMP power supply injected gain has a single dominant
zero at fP±SZ1 , analysis yields
f
1
1+j
αPSRR (0)±
VOU T (f )±
fP±SZ1
=
f
VS
1+j
αGBP
f
1+j
R2
f±
±
± P SZ1 , α =
Where AP S(f ) = AP S(0)
= 1e − 4
f
R1 + R2
1+j
fp1
±
P
SRR(0)
AD (0)
, P SRR(0)+ =
P SRR(f )± = and P SRR(0)− =
+
f
AP S (0)
1+j
±
fP SZ1
30
M. E. Brinson and D. J. Faulkner, Measurement and modelling of operational amplifier power
supply rejection, Int. J. Electronics, 1995, vol. 78, NO. 4, 667-678.
71
2e-4
vout_boyle_orig.v
1.5e-4
1e-4
5e-5
0
1
10
100
1e3
acfrequency
2e-4
vout_boyle_ac.v
1.5e-4
1e-4
5e-5
0
1
10
100
1e3
100
1e3
acfrequency
2e-4
vout_mod.v
1.5e-4
1e-4
5e-5
0
1
10
acfrequency
Figure 55: AC common-mode simulation results for (1) Boyle macromodel, (2) ac
Boyle macromodel and (3) the modular macromodel
72
V3
U=1 V
R1
R=100k
R2
R=10
V1
U=15 V
UA741(Boyle)
+
R3
R=10
vout
VCC
V2
U=15 V
VEE
SUB1
R4
R=100k
dc simulation
ac simulation
DC1
AC1
Type=log
Start=1 Hz
Stop=10 MHz
Points=500
Figure 56: Test circuit for the simulation of PSRR(f) voltage transfer function
characteristic
AD (0)
.
AP S (0)−
Typical values for the UA741 are P SRR(0)+ = 110000, P SRR(0)− = 170000, fP+SZ1 =
685Hz, fP−SZ1 = 6.2Hz. The considerable difference in the dominant zero frequencies of the injected power supply gains is normally due to the fact that the OP
AMP circuits are not symmetric when viewed from the power supply signal injection terminals. By adding external components to an OP AMP macromodel power
supply rejection effects can be easily simulated. The schematic shown in Fig. 57
shows the TI UA741 model with RC networks connected between the power supply terminals and earth. The voltage controlled voltage sources probe the voltages
at the center nodes of the additional RC networks. These networks generate the
power supply injected signals at dc. They also generate the dominant zero in the
power supply rejection characteristic.
The values for the passive components can be calculated using:
RA =
1
106
1
106
,
CA
=
,
RB
=
, CA =
+
+
−
6
6
P SRR(0)
P SRR(0)
2 · 10 · π · fP SZ1
2 · 10 · π · fP−SZ1
Which gives, for the example UA741 device data, RA = 9Ω, CA = 232pF , RB =
5.9Ω and CB = 25.7pF . Simulation waveforms for the small signal frequency
response of the test circuit are shown in Fig. 58. In the case of the modular UA741
model the simulation signal plot clearly demonstrates the fact that the model does
not correctly represent the effects due to power supply injected signals.
73
Vout_mod
dc simulation
R1
R=100k
VS
U=1 V
DC1
-
R2
R=10
UA741
(MOD)
+
R3
R=10
V1
U=15 V
VCC
R4
R=100k
ac simulation
V2
U=15 V
VEE
SUB5
AC1
Type=log
Start=1 Hz
Stop=10 kHz
Points=400
R11
R=100k
CA
C=232p
RA
R=9
R9
R=10
EP2
G=0.5
EN2
G=0.5
R5
R=1M
vout_TI
VCC
UA741(TI)
+
VEE
SUB4
EP1 EN1
G=0.5 G=0.5
R10
R=10
R6
R=1M
RB
R=5.9
R12
R=100k
CB
C=25.7nF
Equation
Eqn1
PSRR_P=dB(p1/(vout_TI.v*p2*alpha))
fpz1=685
alpha=1e-4
gbp=1e-6
p1=mag(1+j*acfrequency/fpz1)
p2=mag(1+j*acfrequency/alpha*gbp)
Figure 57: Test circuit showing OP AMP with external power supply rejection
modelling network
74
0.03
vout_TI.v
0.025
0.02
0.015
0.01
1
10
100
acfrequency
1
10
100
acfrequency
1
10
100
acfrequency
1e3
1e4
PSRR_P
110
105
100
1e3
1e4
Vout_mod.v
3e-21
2e-21
1e-21
0
1e3
1e4
Figure 58: Simulation waveforms for the circuit illustrated in Fig. 57
75
End note
While writing this tutorial I have tried to demonstrate how practical models of
operational amplifiers can be constructed using basic electronic concepts and the
range of Qucs built-in components. The modular OP AMP macromodel was deliberately chosen as the foundation for the tutorial for two reasons; firstly Qucs
is mature enough to easily simulate such models, and secondly the parameters
which determine the operation of the macromodel can be be calculated directly
from information provided on device data sheets. Recent modelling development
by the Qucs team has concentrated on improving the SPICE to Qucs conversion
facilities. This work has had a direct impact on Qucs ability to import and simulate manufacturers OP AMP models. The tutorial upgrade explains how SPICE
Boyle type OP AMP macromodels can be converted to work with Qucs. The Qucs
OP AMP library (OpAmps) has been extended to include models for a range of
popular 8 pin DIL devices. If you require a model with a specific specification that
is not modelled by an available macromodel then adding extra functionality may
be the only way forward. Two procedures for extending models are outlined in the
tutorial upgrade. Much work still remains to be done before Qucs can simulate
a wide range of the macromodels published by device manufacturers. With the
recent addition of subcircuit/component equations to Qucs it is now possible to
write generalised macromodel macros for OP AMPs. However, before this can
be done time is required to fully test the features that Stefan and Michael have
recently added to Qucs release 0.0.11. This topic and the modelling of other OP
AMP properties such as noise will be the subject of a further OP AMP tutorial
update sometime in the future. My thanks to David Faulkner for all his help and
support during the period we were working on a number of the concepts that form
part of the basis of this tutorial. Once again a special thanks to Michael Margraf
and Stefan Jahn for all their help and encouragement over the period that I have
been writing this tutorial and testing the many examples it includes.
76